Relevant bibliographies by topics / Homologie de Khovanov

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Homologie de Khovanov'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Homologie de Khovanov"

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Tubbenhauer, Daniel. "𝔤𝔩n-webs, categorification and Khovanov–Rozansky homologies." Journal of Knot Theory and Its Ramifications 29, no. 11 (October 2020): 2050074. http://dx.doi.org/10.1142/s0218216520500741.

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In this paper, we define an explicit basis for the [Formula: see text]-web algebra [Formula: see text] (the [Formula: see text] generalization of Khovanov’s arc algebra) using categorified [Formula: see text]-skew Howe duality. Our construction is a [Formula: see text]-web version of Hu–Mathas’ graded cellular basis and has two major applications: it gives rise to an explicit isomorphism between a certain idempotent truncation of a thick calculus cyclotomic KLR algebra and [Formula: see text], and it gives an explicit graded cellular basis of the [Formula: see text]-hom space between two [Formula: see text]-webs. We use this to give a (in principle) computable version of colored Khovanov–Rozansky [Formula: see text]-link homology, obtained from a complex defined purely combinatorially via the (thick cyclotomic) KLR algebra and needs only [Formula: see text].
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Robert, Louis-Hadrien, and Emmanuel Wagner. "Symmetric Khovanov-Rozansky link homologies." Journal de l’École polytechnique — Mathématiques 7 (April 2, 2020): 573–651. http://dx.doi.org/10.5802/jep.124.

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Collari, Carlo. "Transverse invariants from Khovanov-type homologies." Journal of Knot Theory and Its Ramifications 28, no. 01 (January 2019): 1950012. http://dx.doi.org/10.1142/s0218216519500123.

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In this paper, we introduce a family of transverse invariants arising from the deformations of Khovanov homology. This family includes the invariants introduced by Plamenevskaya and by Lipshitz, Ng, and Sarkar. Then, we investigate the invariants arising from Bar-Natan’s deformation. These invariants, called [Formula: see text]-invariants, are essentially equivalent to Lipshitz, Ng, and Sarkar’s invariants [Formula: see text]. From the [Formula: see text]-invariants, we extract two non-negative integers which are transverse invariants (the [Formula: see text]-invariants). Finally, we give several conditions which imply the non-effectiveness of the [Formula: see text]-invariants, and use them to prove several vanishing criteria for the Plamenevskaya invariant [Formula: see text], and the non-effectiveness of the vanishing of [Formula: see text], for all prime knots with less than 12 crossings.
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Cautis, Sabin, Aaron D. Lauda, and Joshua Sussan. "Curved Rickard complexes and link homologies." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 769 (December 1, 2020): 87–119. http://dx.doi.org/10.1515/crelle-2019-0044.

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AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).
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Tubbenhauer, Daniel. "Virtual Khovanov homology using cobordisms." Journal of Knot Theory and Its Ramifications 23, no. 09 (August 2014): 1450046. http://dx.doi.org/10.1142/s0218216514500461.

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We extend Bar-Natan's cobordism-based categorification of the Jones polynomial to virtual links. Our topological complex allows a direct extension of the classical Khovanov complex (h = t = 0), the variant of Lee (h = 0, t = 1) and other classical link homologies. We show that our construction allows, over rings of characteristic two, extensions with no classical analogon, e.g. Bar-Natan's ℤ/2-link homology can be extended in two non-equivalent ways. Our construction is computable in the sense that one can write a computer program to perform calculations, e.g. we have written a MATHEMATICA-based program. Moreover, we give a classification of all unoriented TQFTs which can be used to define virtual link homologies from our topological construction. Furthermore, we prove that our extension is combinatorial and has semi-local properties. We use the semi-local properties to prove an application, i.e. we give a discussion of Lee's degeneration of virtual homology.
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Duong, Nguyen D., and Lawrence P. Roberts. "Twisted skein homology." Journal of Knot Theory and Its Ramifications 23, no. 05 (April 2014): 1450027. http://dx.doi.org/10.1142/s0218216514500278.

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We apply the techniques of totally twisted Khovanov homology to Asaeda, Przytycki, and Sikora's construction of Khovanov type homologies for links and tangles in I-bundles over (orientable) surfaces. As a result we describe a chain complex built out of resolutions with only noncontractible circles whose homology is an invariant of the tangle. We use these to understand the δ-graded homology for links with alternating diagrams in the surface.
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MACKAAY, MARCO, PAUL TURNER, and PEDRO VAZ. "A REMARK ON RASMUSSEN'S INVARIANT OF KNOTS." Journal of Knot Theory and Its Ramifications 16, no. 03 (March 2007): 333–44. http://dx.doi.org/10.1142/s0218216507005312.

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Dolotin, V., and A. Morozov. "Introduction to Khovanov Homologies. II. Reduced Jones superpolynomials." Journal of Physics: Conference Series 411 (January 28, 2013): 012013. http://dx.doi.org/10.1088/1742-6596/411/1/012013.

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Naisse, Grégoire, and Pedro Vaz. "2-Verma modules and the Khovanov–Rozansky link homologies." Mathematische Zeitschrift 299, no. 1-2 (January 12, 2021): 139–62. http://dx.doi.org/10.1007/s00209-020-02658-7.

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Dolotin, V., and A. Morozov. "Introduction to Khovanov homologies. III. A new and simple tensor-algebra construction of Khovanov–Rozansky invariants." Nuclear Physics B 878 (January 2014): 12–81. http://dx.doi.org/10.1016/j.nuclphysb.2013.11.007.

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Dissertations / Theses on the topic "Homologie de Khovanov"

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Wagner, Emmanuel. "On Khovanov-Rozansky homology of graphs and links." Université Louis Pasteur (Strasbourg) (1971-2008), 2007. https://publication-theses.unistra.fr/restreint/theses_doctorat/2007/WAGNER_Emmanuel_2007.pdf.

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Cette thèse est consacrée à la catégorification d'invariants polynomiaux d'entrelacs et de graphes. Pour tout entier strictement positif n, Khovanov et Rozansky ont introduit en 2004 une homologie bigraduée d'entrelacs, ainsi qu'une homologie de graphes planaires. Etant donné n, leur homologie d'entrelacs catégorifie la n-ième spécialisation du polynôme d'entrelacs HOMFLYPT et leur homologie de graphes planaires catégorifie un polynôme de graphes associé. Dans cette thèse, on étudie ces homologies et on généralise leur construction en introduisant une graduation supplémentaire. Tout d'abord, on généralise une formule de Jaeger pour les polynômes d'entrelacs aux polynômes de graphes planaires, ainsi qu'à l'homologie de graphes planaires; on étend ensuite l'homologie d'entrelacs de Khovanov-Rozansky aux graphes plongés. Puis on construit une homologie trigraduée d'entrelacs. Cette homologie recouvre l'homologie bigraduée d'entrelacs de Khovanov et Rozansky. Enfin, on donne des exemples, des applications et des généralisations de l'homologie trigraduée d'entrelacs. On développe des outils d'algèbre homologique qui permettent de calculer explicitement l'homologie trigraduée d'entrelacs pour des exemples et on considère des déformations de l'homologie trigraduée d'entrelacs
This thesis is devoted to the categorification of polynomial invariants of graphs and links. For any positive integer n, Khovanov and Rozansky introduced in 2004 a bigraded link homology, and an homology of planar graphs. Given n, their link homology categorifies the n-th specialization of the HOMFLY-PT polynomial and their homology of planar graphs categorifies an associated graph polynomial. In this thesis, we study these homology and generalize their constructions by introducing an additional grading. First, we generalize a formula of Jaeger for link polynomials to polynomials of planar graphs and associated homology of planar graphs; we extend also the link homology of Khovanov and Rozansky to embedded graphs. Then we construct a triply graded link homology. This homology recovers the bigraded link homology of Khovanov and Rozansky. Finally, we give examples, applications and generalizations of the triply graded link homology. We develop homological tools that permit to compute explicitly the triply graded link homology for some knots and we consider deformations of the triply graded link homology
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Wagner, Emmanuel Touraev Vladimir G. "On Khovanov-Rozansky homology of graphs and links." Strasbourg : Université Louis Pasteur, 2008. http://eprints-scd-ulp.u-strasbg.fr:8080/00000912.

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Lewark, Lukas. "Homologies de Khovanov-Rozansky, toiles nouées pondérées et genre lisse." Paris 7, 2013. http://www.theses.fr/2013PA077117.

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Cette thèse porte sur les homologies de Khovanov-Rozansky et les invariants de concordance des nœuds qui en proviennent, en prêtant une attention particulière à l'homologie s13 définie par des mousses. Le premier chapitre est consacré aux interdépendances des différentes homologies de Khovanov-Rozansky : les homologies non-réduite et réduite, graduée et filtrée, et les homologies Homflypt et slN pour différents valeurs de N. Grâce à une composition des suites spectrales connues et nouvelles, on démontre sur des exemples que les invariants de concordance slN ne sont pas tous égaux ; ce résultat constitue une réponse à un problème ouvert jusqu'à ici. Le deuxième et troisième chapitres présentent une implémentation d'un algorithme qui calcule l'homologie s!3. Hormis le programme de Bar-Natan, Green et Morrison, donnant l'homologie de Khovanov, il s'agit du seul programme pour calculer une des homologies de Khovanov-Rozansky d'une manière efficace. Les calculs démontrent que l'invariant de concordance s13 peut prendre des valeurs impaires. Dans le quatrième chapitre, les homologies s!3 graduées et filtrées sont étendues à une classe des graphes noués et F3- pondérés : les toiles nouées pondérées. Les mousses pondérables, qui jouent le rôle des cobordismes orientables pour les toiles pondérées, permettent de définir la notion de degré lisse pour des toiles nouées pondérées. Par analogie avec le travail de Rasmussen, on démontre qu'une borne inférieure au degré lisse des toiles nouées pondérées découle de l'homologie s13 filtrée
This thesis focuses on the Khovanov-Rozansky homologies and the knot concordance invariants issuing from them, paying particular attention to the s13-foam homology. The first chapter treats the interrelation of different Khovanov-Rozansky homologies: unreduced and reduced, graded and filtered, and categorifying the Homflypt-polynomial and the slN-polynomial for varying N. A combination of new and known spectral sequences allows to show exemplarily that the slN-knot concordance invariants may differ, which was unknown until now. In the second and third chapter, an implementation of an algorithm Computing s13-homology is presented. Aside from Bar-Natan, Green and Morrisons' programme calculating Khovanov homology, this is the only existing programme that efficiently computes any Khovanov-Rozansky homology theory. Its calculations show that the s!3-knot concordance invariant may be an odd integer. In the fourth chapter, graded and filtered s!3-homology are generalised to a class of knotted F3-weighted graphs, called knotted weighted webs. Weightable foams are defined, which are to knotted weighted webs what orientable cobordisms are to knots, and the slice degree of knotted weighted webs is introduced. In analogy with Rasmussen's result, it is shown that the filtered sl3-homology yields a lower bound for the slice degree of knotted weighted webs
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Robert, Louis-Hadrien. "Sur l'homologie sl3 des enchevêtrements : algèbres de Khovanov - Kuperberg." Paris 7, 2013. http://www.theses.fr/2013PA077240.

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Cette thèse est consacrée aux algèbres de Khovanov-Kuperberg Kc et à leurs catégories de modules. Ce sont les analogues dans le cas s13 , des algèbres H n utilisées par Khovanov pour étendre l'homologie s12 (ou homologie de Khovanov) aux enchevêtrements. Elles apparaissent comme les images des 0-objets par une (0+1+1)-TQFT. Elles permettent de définir une homologie s13 aux enchevêtrements. Ces algèbres ont des catégories de modules particulièrement intéressantes : du fait même de leurs constructions, elles sont profondément liées à l'étude des bases de certaines représentations du groupe quantique Uq(s13 ). Il est alors naturel de vouloir classifier les modules projectifs indécomposables sur ces algèbres. Nous étudions les modules de toiles qui sont des Kr -modules projectifs. Il a été conjecturé que ces modules formaient une famille complète de représentants des classes d'isomorphismes de Kc-modules projectifs indécomposables, mais Khovanov et Kuperberg ont exhibé un module de toile qui se décompose. Dans cette thèse nous donnons deux condition sur l'indécomposabilité des modules de toiles : une condition suffisante de nature géométrique, et une condition nécessaire et suffisante de nature algébrique. Les résultats sont prouvés d'une part grâce à une étude combinatoire des toiles, qui sont des graphes trivalents bipartites plan et d'un polynôme de Laurent qui leur est associé, le Crochet de Kuperberg. Et d'autre part, grâce à l'étude des mousses qui jouent le rôle de cobordismes pour les toiles
This thesis is concerned with the Khovanov-Kuperberg algebras Ke and to their categories of modules. They are analogous, in the s13 context, to the H n algebras used by Khovanov to extend the s12 -homology (or Khovanov homology) to tangles. They appear as images of the 0-objects by a (0+1+1)-TQFT. They allow to define a s13 -homology for tangles. The categories of modules over: these algebras are especially interesting: from their own construction they are deeply connected to bases in some representations of the quantum group Uq(s13). It is hence natural to ask for a classification of the projective indecomposable modules over these algebras. We study web modules which are projective Kc -modules. It has been conjectured that these modules constitute a complete family of indecomposable projective KE -modules, but Khovanov and Kuperberg have exhibited a web module which decomposes as a direct sum. In this thesis we give two conditions on the indecomposability of web modules: a geometric sufficient condition and an algebraic necessary and sufficient condition. The results are proven on the one hand, through a combinatorial analysis of webs which are plane bicubic graphs, and of Laurent polynomial associated with each web called the Kuperberg bracket. And on the other hand, thanks to foams which plays the role of cobordisms for webs
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Wagner, Emmanuel. "Sur l'homologie de Khovanov-Rozansky des graphes et des entrelacs." Phd thesis, Université Louis Pasteur - Strasbourg I, 2007. http://tel.archives-ouvertes.fr/tel-00192447.

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Cette thèse est consacrée à la catégorification d'invariants polynomiaux d'entrelacs et de graphes. Pour tout entier strictement positif n, Khovanov et Rozansky ont introduit en 2004 une homologie bigraduée d'entrelacs, ainsi qu'une homologie de graphes planaires. Etant donné n, leur homologie d'entrelacs catégorifie la n-ième spécialisation du polynôme d'entrelacs HOMFLYPT et leur homologie de graphes planaires catégorifie un polynôme de graphes associé.

Dans cette thèse, on étudie ces homologies et on généralise leur construction en introduisant une graduation supplémentaire. Tout d'abord, on généralise une formule de Jaeger pour les polynômes d'entrelacs aux polynômes de graphes planaires, ainsi qu'à l'homologie de graphes planaires; on étend ensuite l'homologie d'entrelacs de Khovanov-Rozansky aux graphes plongés. Puis on construit une homologie trigraduée d'entrelacs. Cette homologie recouvre l'homologie bigraduée d'entrelacs de Khovanov et Rozansky. Enfin, on donne des exemples, des applications et des généralisations de l'homologie trigraduée d'entrelacs. On développe des outils d'algèbre homologique qui permettent de calculer explicitement l'homologie trigraduée d'entrelacs pour des exemples et on considère des déformations de l'homologie trigraduée d'entrelacs.
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Wagner, Emmanuel Turaev Vladimir G. "Sur l'homologie de Khovanov-Rozansky des graphes et des entrelacs /." Paris, 2007. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=016808065&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Audoux, Benjamin. "Généralisation de l'homologie de Heegaard-Floer aux entrelacs singuliers & raffinement de l'homologie de Khovanov aux entrelacs restreints." Toulouse 3, 2007. http://thesesups.ups-tlse.fr/145/.

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La catégorification d'un invariant polynomial d'entrelacs I est un invariant de type homologique dont la caractéristique d'Euler gradue est égale à I. On pourra citer la catégorification originelle du polynôme de Jones par M. Khovanov ou celle du polynôme d'Alexander par P. Ozsvath et Z. Szabo. Outre leur capacité accrue à distinguer les noeuds, ces nouveaux invariants de type homologique semblent drainer beaucoup d'informations d'ordre géométrique. D'autre part, suite aux travaux de I. Vassiliev dans les années 90, un invariant polynomial d'entrelacs peut être étudié à l'aune de certaines propriétés, dites de type fini, de son extension naturelle aux entrelacs singuliers, c'est-à-dire aux entrelacs possédant un nombre fini de points doubles transverses. La première partie de cette thèse s'intéresse aux liens éventuels entre ces deux procédés, dans le cas particulier du polynôme d'Alexander. Dans cette optique, nous donnons d'abord une description des entrelacs singuliers par diagrammes en grilles. Nous l'utilisons ensuite pour généraliser l'homologie de Ozsvath et Szabo aux entrelacs singuliers. Outre la cohérence de sa définition, nous montrons que cet invariant devient acyclique sous certaines conditions annulant naturellement sa caractéristique d'Euler. Ce travail s'insère dans un programme plus vaste de catégorification des théories de Vassiliev. Dans une seconde partie, nous nous proposons de raffiner l'homologie de Khovanov aux entrelacs restreints. Ces derniers correspondent aux diagrammes d'entrelacs quotientés par un nombre restreint de mouvements de Reidemeister. Les tresses fermées apparaissent notamment comme sous-ensemble de ces entrelacs restreints. Un tel raffinement de l'homologie de Khovanov offre donc un nouvel outil pour une étude plus ciblée des noeuds et de leurs déformations
A categorification of a polynomial link invariant is an homological invariant which contains the polynomial one as its graded Euler characteristic. This field has been initiated by Khovanov categorification of the Jones polynomial. Later, P. Ozsvath and Z. Szabo gave a categorification of Alexander polynomial. Besides their increased abilities for distinguishing knots, this new invariants seem to carry many geometrical informations. On the other hand, Vassiliev works gives another way to study link invariant, by generalizing them to singular links i. E. Links with a finite number of rigid transverse double points. The first part of this thesis deals with a possible relation between these two approaches in the case of the Alexander polynomial. To this purpose, we extend grid presentation for links to singular links. Then we use it to generalize Ozsvath and Szabo invariant to singular links. Besides the consistency of its definition, we prove that this invariant is acyclic under some conditions which naturally make its Euler characteristic vanish. This work can be considered as a first step toward a categorification of Vassiliev theory. In a second part, we give a refinement of Khovanov homology to restricted links. .
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Zhang, Melissa. "Localization for Khovanov homologies:." Thesis, Boston College, 2019. http://hdl.handle.net/2345/bc-ir:108470.

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Thesis advisor: Julia Elisenda Grigsby
Thesis advisor: David Treumann
In 2010, Seidel and Smith used their localization framework for Floer homologies to prove a Smith-type rank inequality for the symplectic Khovanov homology of 2-periodic links in the 3-sphere. Hendricks later used similar geometric techniques to prove analogous rank inequalities for the knot Floer homology of 2-periodic links. We use combinatorial and space-level techniques to prove analogous Smith-type inequalities for various flavors of Khovanov homology for periodic links in the 3-sphere of any prime periodicity. First, we prove a graded rank inequality for the annular Khovanov homology of 2-periodic links by showing grading obstructions to longer differentials in a localization spectral sequence. We remark that the same method can be extended to p-periodic links. Second, in joint work with Matthew Stoffregen, we construct a Z/p-equivariant stable homotopy type for odd and even, annular and non-annular Khovanov homologies, using Lawson, Lipshitz, and Sarkar's Burnside functor construction of a Khovanov stable homotopy type. Then, we identify the fixed-point sets and apply a version of the classical Smith inequality to obtain spectral sequences and rank inequalities relating the Khovanov homology of a periodic link with the annular Khovanov homology of the quotient link. As a corollary, we recover a rank inequality for Khovanov homology conjectured by Seidel and Smith's work on localization and symplectic Khovanov homology
Thesis (PhD) — Boston College, 2019
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
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Söderberg, Christoffer. "Khovanov Homology of Knots." Thesis, Uppsala universitet, Algebra och geometri, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-325842.

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McDougall, Adam Corey. "Relating Khovanov homology to a diagramless homology." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/709.

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A homology theory is defined for equivalence classes of links under isotopy in the 3-sphere. Chain modules for a link L are generated by certain surfaces whose boundary is L, using surface signature as the homological grading. In the end, the diagramless homology of a link is found to be equal to some number of copies of the Khovanov homology of that link. There is also a discussion of how one would generalize the diagramless homology theory (hence the theory of Khovanov homology) to links in arbitrary closed oriented 3-manifolds.
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Books on the topic "Homologie de Khovanov"

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Witten, Edward. Two Lectures on the Jones Polynomial and Khovanov Homology. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198784913.003.0001.

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In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The variable q is associated to instanton number in the dual description in four dimensions. In the second lecture, I describe how Khovanov homology can emerge upon adding a fifth dimension.
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Book chapters on the topic "Homologie de Khovanov"

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Shumakovitch, Alexander. "Khovanov Homology Theories and Their Applications." In Progress in Mathematics, 403–30. Boston, MA: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8277-4_17.

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Kauffman, Louis H. "Remarks on Khovanov Homology and the Potts Model." In Progress in Mathematics, 237–62. Boston, MA: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8277-4_11.

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Przytycki, Józef H. "Knot Theory: From Fox 3-Colorings of Links to Yang–Baxter Homology and Khovanov Homology." In Knots, Low-Dimensional Topology and Applications, 115–45. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16031-9_5.

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Kauffman, Louis H. "KHOVANOV HOMOLOGY." In Introductory Lectures on Knot Theory, 248–80. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814313001_0010.

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"Khovanov Homology." In Virtual Knots, 177–256. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814401135_0005.

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"Khovanov homology and torsion." In New Directions in Geometric and Applied Knot Theory, 125–37. De Gruyter Open Poland, 2017. http://dx.doi.org/10.1515/9783110571493-006.

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Manturov, Vassily. "Khovanov homology of virtual knots." In Knot Theory, 393–442. CRC Press, 2018. http://dx.doi.org/10.1201/9780203710920-22.

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Conference papers on the topic "Homologie de Khovanov"

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Witten, Edward. "Khovanov homology and gauge theory." In Low-dimensional manifolds and high-dimensional categories -- A conference in honor of Michael Hartley Freedman. Mathematical Sciences Publishers, 2012. http://dx.doi.org/10.2140/gtm.2012.18.291.

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CHBILI, Nafaa. "TOWARD AN EQUIVARIANT KHOVANOV HOMOLOGY." In Intelligence of Low Dimensional Topology 2006 - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770967_0003.

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LIPSHITZ, ROBERT, and SUCHARIT SARKAR. "SPATIAL REFINEMENTS AND KHOVANOV HOMOLOGY." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0091.

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Manturov, Vassily Olegovich. "Additional Gradings in Khovanov Homology." In Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812819116_0013.

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Kauffman, Louis H., and Samuel J. Lomonaco. "Quantum algorithms for the Jones polynomial and Khovanov homology." In SPIE Defense, Security, and Sensing. SPIE, 2012. http://dx.doi.org/10.1117/12.918987.

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6

Vélez, Mario, and Juan Ospina. "Possible universal quantum algorithms for generalized Khovanov homology and the Rasmussen's invariant." In SPIE Defense, Security, and Sensing. SPIE, 2012. http://dx.doi.org/10.1117/12.918886.

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7

Ospina, Juan. "Possible quantum algorithm for the Lipshitz-Sarkar-Steenrod square for Khovanov homology." In SPIE Defense, Security, and Sensing, edited by Eric Donkor, Andrew R. Pirich, and Howard E. Brandt. SPIE, 2013. http://dx.doi.org/10.1117/12.2016298.

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Vélez, Mario, and Juan Ospina. "Possible topological quantum computation via Khovanov homology: D-brane topological quantum computer." In SPIE Defense, Security, and Sensing, edited by Eric J. Donkor, Andrew R. Pirich, and Howard E. Brandt. SPIE, 2009. http://dx.doi.org/10.1117/12.818551.

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