Relevant bibliographies by topics / Non-commutative topology

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Academic literature on the topic 'Non-commutative topology'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Non-commutative topology"

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Solovyov, Sergey A. "Generalized fuzzy topology versus non-commutative topology." Fuzzy Sets and Systems 173, no. 1 (2011): 100–115. http://dx.doi.org/10.1016/j.fss.2011.03.005.

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Bauer, Andrej, Karin Cvetko-Vah, Mai Gehrke, Samuel J. van Gool, and Ganna Kudryavtseva. "A non-commutative Priestley duality." Topology and its Applications 160, no. 12 (2013): 1423–38. http://dx.doi.org/10.1016/j.topol.2013.05.012.

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Wu, Wei. "Non-commutative metric topology on matrix state space." Proceedings of the American Mathematical Society 134, no. 02 (2005): 443–53. http://dx.doi.org/10.1090/s0002-9939-05-08036-6.

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Goldstein, Stanisław. "Conditional expectation and stochastic integrals in non-commutative Lp spaces." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 2 (1991): 365–83. http://dx.doi.org/10.1017/s0305004100070432.

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The aim of the paper is to propose a general scheme for the consideration of non-commutative stochastic integrals. The role of a probability space is played by a couple (, φ0), where is a von Neumann algebra and φ0 is a faithful normal state on . Our processes live in the algebra of all measurable operators associated with the crossed product of by the modular automorphism group The algebra contains all the (Haagerup's) Lp spaces over . The measure topology of the algebra has the nice feature of inducing the Lp norm topology on the Lp spaces, which makes it particularly suitable for defining stochastic integrals. The commutative theory fits smoothly into the scheme, although there exists no canonical way of embedding the algebra of (commutative) random variables into . In fact, for any commutative stochastic process we have a family of different non-commutative stochastic processes corresponding to the process. This arbitrariness seems to be quite natural in the non-commutative context. An appropriate example can be found at the end of the paper (Section 6, C4).
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Schweizer, J. "An Analogue of Peetre's Theorem in Non-Commutative Topology." Quarterly Journal of Mathematics 52, no. 4 (2001): 499–506. http://dx.doi.org/10.1093/qjmath/52.4.499.

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De Nittis, Giuseppe, and Hermann Schulz-Baldes. "The non-commutative topology of two-dimensional dirty superconductors." Journal of Geometry and Physics 124 (January 2018): 100–123. http://dx.doi.org/10.1016/j.geomphys.2017.10.016.

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Georgescu, G., and A. Popescu. "Non-commutative fuzzy Galois connections." Soft Computing 7, no. 7 (2003): 458–67. http://dx.doi.org/10.1007/s00500-003-0280-4.

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GAROUFALIDIS, STAVROS, and XINYU SUN. "THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS." Journal of Knot Theory and Its Ramifications 19, no. 12 (2010): 1571–95. http://dx.doi.org/10.1142/s021821651000856x.

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The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative A-polynomial of twist knots. Our multivariable creative telescoping method allows us to compute linear recursions for sums of the form [Formula: see text] given a recursion relation for [Formula: see text] and the hypergeometric kernel c(n, k). As an application of our method, we explicitly compute the non-commutative A-polynomial for twist knots with -15 and 15 crossings. The non-commutative A-polynomial of a knot encodes the monic, linear, minimal order q-difference equation satisfied by the sequence of colored Jones polynomials of the knot. Its specialization to q = 1 is conjectured to be the better-known A-polynomial of a knot, which encodes important information about the geometry and topology of the knot complement. Unlike the case of the Jones polynomial, which is easily computable for knots with 50 crossings, the A-polynomial is harder to compute and already unknown for some knots with 12 crossings.
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Junge, M. "Embeddings of non-commutative L p -spaces into non-commutative L 1 -spaces, 1 < p < 2." Geometric And Functional Analysis 10, no. 2 (2000): 389–406. http://dx.doi.org/10.1007/s000390050012.

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Szendrői, Balázs. "Non-commutative Donaldson–Thomas invariants and the conifold." Geometry & Topology 12, no. 2 (2008): 1171–202. http://dx.doi.org/10.2140/gt.2008.12.1171.

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Dissertations / Theses on the topic "Non-commutative topology"

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Aeal, Wemedh. "K-theory, chamber homology and base change for the p-ADIC groups SL(2), GL(1) and GL(2)." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/ktheory-chamber-homology-and-base-change-for-the-lowercasepadic-groups-sl2-gl1-and-gl2(974c74a7-83ff-4cb2-bbb8-e15cfbb8e2e1).html.

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The thrust of this thesis is to describe base change BC_E/F at the level of chamber homology and K-theory for some p-adic groups, such as SL(2,F), GL(1,F) and GL(2,F). Here F is a non-archimedean local field and E is a Galois extension of F. We have had to master the representation theory of SL(2) and GL(2) including the Langlands parameters. The main result is an explicit computation of the effect of base change on the chamber homology groups, each of which is constructed from cycles. This will have an important connection with the Baum-Connes correspondence for such p-adic groups. This thesis involved the arithmetic of fields such as E and F, geometry of trees, the homology groups and the Weil group W_F.
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Zarrouati, Marc. "Contributions à la topologie non commutative des solides apériodiques." Toulouse 3, 2000. http://www.theses.fr/2000TOU30212.

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Martinetti, Pierre. "Distances en géométrie non commutative." Aix-Marseille 1, 2001. http://www.theses.fr/2001AIX11032.

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Cette thèse étudie l'aspect métrique de la géométrie non commutative à travers la formulation de Connes de la distance entre états d'une algèbre. La définition d'un espace non commutatif<br>Cette thèse étudie l'aspect métrique de la géométrie non commutative à travers la formulation de Connes de la distance entre états d'une algèbre. La définition d'un espace non commutatif est l'objet du premier chapitre. Des propriétés générales de la formule de la distance sont mises en évidence ainsi que d'importantes simplifications quand l'algèbre est de von Neumann. Dans le deuxième chapitre, les distances sont calculées pour des algèbres de dimension finie. Les cas "Cn" et "Mn(C)" sont envisagés. Dans le troisième chapitre, on étudie la distance pour des géométries obtenues par produit de l'espace-temps riemannien avec une géométrie discrète. Des conditions sont établies garantissant que l'espace discret soit orthogonal, au sens du théorème de Pythagore, à l'espace continu. On obtient ainsi une description complète de la métrique pour un exemple de base de la géométrie non commutative, le modèle à deux couches. On montre également en toute généralité que la métrique d'une géométrie n'est pas perturbée quand on réalise son produit avec une autre géométrie. Le dernier chapitre étudie l'évolution de la métrique lorsque la géométrie est perturbée par des champs de jauges. En se limitant à la partie scalaire de ces champs, on calcule les distances dans la géométrie du modèle standard. Il apparaît que le champ de Higgs est le coefficient d'une métrique riemannienne dans un espace de dimension 4 (continues) + 1 (discrète)
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Cagnache, Eric. "Aspects différentiels et métriques de la géométrie non commutative : application à la physique." Thesis, Paris 11, 2012. http://www.theses.fr/2012PA112115.

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La géométrie non commutative, du fait qu'elle permet de généraliser des objets géométriques sous forme algébrique, offre des perspectives intéressantes pour réunir la théorie quantique des champs et la relativité générale dans un seul cadre. Elle peut être abordée selon différents points de vue et deux d'entre eux sont présentés dans cette thèse. Le premier, le calcul différentiel basé sur les dérivations, nous a permis de construire une action de Yang-Mills-Higgs dans laquelle apparait des champs pouvant être interprétés comme des champs de Higgs. Avec le second, les triplets spectraux, on peut généraliser la notion de distance entre état et calculer des formules de distance. C'est ce que nous avons fait dans le cas de l'espace de Moyal et du tore non commutatif<br>Noncommutative geometry offers interesting prospects to gather the quantum field theory and relativity in one general framework because it allows one to generalize geometric objects algebraically. It can be approached from different points of view and two of them are presented in this PhD. The first, calculus based on derivations, allowed us to construct a Yang-Mills-Higgs action which appears in fields that can be interpreted as Higgs fields. With the second, spectral triples, we can generalize the notion of distance between states. We calculated the distance formulas in the case of the Moyal space and the noncommutative torus
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Julien, Antoine. "Complexité des pavages apériodiques : calculs et interprétations." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00466323.

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La théorie des pavages apériodiques a connu des développements rapides depuis les années 1980, avec la découvertes d'alliages métalliques cristallisant dans une structure quasi-périodique.Dans cette thèse, on étudie particulièrement deux méthodes de construction de pavages : par coupe et projection, et par substitution. Deux angles d'approche sont développés : l'étude de la fonction de complexité, et l'étude métrique de l'espace de pavages.Dans une première partie, on calcule l'asymptotique de la fonction de complexité pour des pavages coupe et projection, généralisant ainsi des résultats connus en dynamiques symbolique pour la dimension 1. On montre que pour un pavage coupe et projection canonique N sur d sans période, la complexité croît (à des constantes près) comme n à la puissance a, où a est un entier compris entre d et N-d.Ensuite, on se base sur une construction de Pearson et Bellissard qui construisent un triplet spectral sur les ensembles de Cantor ultramétriques. On suit leur construction dans le cas d'ensembles de Cantor auto-similaires. Elle s'applique en particulier aux transversales d'espaces de pavages de substitution.Enfin, on fait le lien entre la distance usuelle sur l'enveloppe d'un pavage et la complexité de ce pavage. Les liens entre complexité et métrique permettent de donner une preuve directe du fait suivant : la complexité des pavages de substitution apériodiques de dimension d croît comme n à la puissance d.La question de liens entre la complexité et la topologie (et pas seulement avec la distance) reste ouverte. Nous apportons cependant des réponses partielles dans cette direction.
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Moustafa, Haïja. "Gap-labeling des pavages de type pinwheel." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2009. http://tel.archives-ouvertes.fr/tel-00509886.

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Dans cette thèse, nous montrons que le groupe de K-théorie $K_0$ de la $C^*$-algèbre associée aux pavages de type pinwheel est isomorphe à la somme de $\ZZ \oplus \ZZ^6$ et d'un groupe cohomologique $H$.\\ Cette $C^*$-algèbre est de plus munie d'une trace qui induit une application linéaire sur ce groupe de $K$-théorie.\\ Nous calculons explicitement l'image, sous cette application, du sommant $\ZZ \oplus \ZZ^6$, montrant que l'image de $\ZZ$ est nulle et que l'image de $\ZZ^6$ est contenue dans le module de fréquences des patchs du pavage de type pinwheel.\\ Nous montrons également que l'on peut appliquer le théorème de l'indice mesuré dû à A. Connes pour relier l'image de $H$ à une formule cohomologique plus calculable.\\ Pour l'étude de cette partie cohomologique, nous adaptons la cohomologie PV, introduite par J. Savinien et J. Bellissard, au cas des pavages de type pinwheel pour montrer que le groupe de cohomologie de \v{C}ech de dimension maximale de ces pavages est isomorphe au groupe des coinvariants entiers de la transversale canonique associée à ces pavages.\\ Ce résultat nous permet alors de prouver la conjecture du gap-labeling fait par J. Bellissard, dans le cas particulier des pavages de type pinwheel.\\ Nous terminons cette étude par un calcul explicite, montrant que le gap-labeling (ou module de fréquences des patchs) est donné par $\frac{1}{264}\ZZ \left [ \frac{1}{5} \right ]$.
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Franklin, Bridget. "Obstructions to the Concordance of Satellite Knots." Thesis, 2012. http://hdl.handle.net/1911/64620.

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Formulas which derive common concordance invariants for satellite knots tend to lose information regarding the axis a of the satellite operation R(a,J). The Alexander polynomial, the Blanchfield linking form, and Casson-Gordon invariants all fail to distinguish concordance classes of satellites obtained by slightly varying the axis. By applying higher-order invariants and using filtrations of the knot concordance group, satellite concordance may be distinguished by determining which term of the derived series of the fundamental group of the knot complement the axes lie. There is less hope when the axes lie in the same term. We introduce new conditions to distinguish these latter classes by considering the axes in higher-order Alexander modules in three situations. In the first case, we find that R(a,J) and R(b,J) are non-concordant when a and b have distinct orders viewed as elements of the classical Alexander module of R. In the second, we show that R(a,J) and R(b,J) may be distinguished when the classical Blanchfield form of a with itself differs from that of b with itself. Ultimately, this allows us to find infinitely many concordance classes of R(-,J) whenever R has nontrivial Alexander polynomial. Finally, we find sufficient conditions to distinguish these satellites when the axes represent equivalent elements of the classical Alexander module by analyzing higher-order Alexander modules and localizations thereof.
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Hudson, Daniel. "K-theory correspondences and the Fourier-Mukai transform." Thesis, 2019. http://hdl.handle.net/1828/10837.

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The goal of this thesis is to give an introduction to the geometric picture of bivariant K-theory developed by Emerson and Meyer building on the ideas Connes and Skandalis, and then to apply this machinery to give a geometric proof of a result of Emerson. We begin by giving an overview of topological K-theory, necessary for developing bivariant K-theory. Then we discuss Kasparov's analytic bivariant K-theory, and from there develop topological bivariant K-theory. In the final chapter we state and prove the result of Emerson.<br>Graduate
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Nadareishvili, George. "A classification of localizing subcategories by relative homological algebra." Doctoral thesis, 2015. http://hdl.handle.net/11858/00-1735-0000-0028-867A-A.

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Books on the topic "Non-commutative topology"

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Ranicki, Andrew, ed. Non-Commutative Localization in Algebra and Topology. Cambridge University Press, 2006. http://dx.doi.org/10.1017/cbo9780511526381.

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Teleman, Neculai S. From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6.

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Strong limit theorems in non-commutative probability. Springer-Verlag, 1985.

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Caribbean Spring School of Mathematics and Theoretical Physics (1st 1993 Saint François, Guadeloupe). Infinite dimensional geometry, non commutative geometry, operator algebras, fundamental interactions: First Caribbean Spring School of Mathematics and Theoretical Physics, Saint François-Guadeloupe, May 30-June 13, 1993. Edited by Coquereaux Robert, Dubois-Violette M, and Flad P. World Scientific, 1995.

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A non-Hausdorff completion: The Abelian category of C-complete left modules over a topological ring. World Scientific, 2015.

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1948-, Ranicki Andrew, ed. Non-commutative localization in algebra and topology. Cambridge University Press, 2006.

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Teleman, Neculai S. From Differential Geometry to Non-commutative Geometry and Topology. Springer, 2020.

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Teleman, Neculai S. From Differential Geometry to Non-commutative Geometry and Topology. Springer, 2019.

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(Editor), P. Flad, ed. Infinite Dimensional Geometry Non Commutative Geometry Operator Algebras Fundamental Interactions: Saint Francois-Guadeloupe May 30-June 13, 1993. World Scientific Pub Co Inc, 1995.

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Book chapters on the topic "Non-commutative topology"

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Teleman, Neculai S. "Non-commutative Topology." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_10.

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Teleman, Neculai S. "Index Theorems in Non-commutative Geometry." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_6.

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Teleman, Neculai S. "Spaces, Bundles and Characteristic Classes in Differential Geometry." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_1.

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Teleman, Neculai S. "Spaces, Bundles, Homology/Cohomology and Characteristic Classes in Non-commutative Geometry." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_2.

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Teleman, Neculai S. "Hochschild, Cyclic and Periodic Cyclic Homology." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_3.

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Teleman, Neculai S. "Analytic Structures on Topological Manifolds." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_4.

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Teleman, Neculai S. "Index Theorems in Differential Geometry." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_5.

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Teleman, Neculai S. "Algebraic Structures." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_7.

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Teleman, Neculai S. "Topological Index and Analytical Index: Reformulation of Index Theory." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_8.

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Teleman, Neculai S. "Local Hochschild Homology of the Algebra of Hilbert–Schmidt Operators on Simplicial Spaces." In From Differential Geometry to Non-commutative Geometry and Topology. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28433-6_9.

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