Relevant bibliographies by topics / Homotopic algebra

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

Academic literature on the topic 'Homotopic algebra'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 February 2022

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Journal articles on the topic "Homotopic algebra"

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Blackadar, Bruce. "The Homotopy Lifting Theorem for Semiprojective $C^*$-Algebras." MATHEMATICA SCANDINAVICA 118, no. 2 (2016): 291. http://dx.doi.org/10.7146/math.scand.a-23691.

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We prove a complete analog of the Borsuk Homotopy Extension Theorem for arbitrary semiprojective $C^*$-algebras. We also obtain some other results about semiprojective $C^*$-algebras: a partial lifting theorem with specified quotient, a lifting result for homomorphisms close to a liftable homomorphism, and that sufficiently close homomorphisms from a semiprojective $C^*$-algebra are homotopic.
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Casals, Roger, Álvaro del Pino, and Francisco Presas. "Loose Engel structures." Compositio Mathematica 156, no. 2 (2020): 412–34. http://dx.doi.org/10.1112/s0010437x19007759.

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This paper contributes to the study of Engel structures and their classification. The main result introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete $h$-principle when auxiliary data is fixed. As a corollary, we show that Lorentz and orientable Cartan prolongations are classified up to homotopy by their formal data.
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HIROSE, SUSUMU, and AKIRA YASUHARA. "REGULAR HOMOTOPIC DEFORMATION OF COMPACT SURFACE WITH BOUNDARY AND MAPPING CLASS GROUP." Journal of Knot Theory and Its Ramifications 20, no. 10 (2011): 1391–96. http://dx.doi.org/10.1142/s021821651100925x.

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A necessary and sufficient algebraic condition for a diffeomorphism over a surface embedded in S3 to be induced by a regular homotopic deformation is discussed, and a formula for the number of signed pass moves needed for this regular homotopy is given.
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Fisette, Robert, and Alexander Polishchuk. "-algebras associated with curves and rational functions on . I." Compositio Mathematica 150, no. 4 (2014): 621–67. http://dx.doi.org/10.1112/s0010437x13007574.

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AbstractWe consider the natural$A_{\infty }$-structure on the$\mathrm{Ext}$-algebra$\mathrm{Ext}^*(G,G)$associated with the coherent sheaf$G=\mathcal{O}_C\oplus \mathcal{O}_{p_1}\oplus \cdots \oplus \mathcal{O}_{p_n}$on a smooth projective curve$C$, where$p_1,\ldots,p_n\in C$are distinct points. We study the homotopy class of the product$m_3$. Assuming that$h^0(p_1+\cdots +p_n)=1$, we prove that$m_3$is homotopic to zero if and only if$C$is hyperelliptic and the points$p_i$are Weierstrass points. In the latter case we show that$m_4$is not homotopic to zero, provided the genus of$C$is greater th
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COSTANTINO, FRANCESCO. "BRANCHED SHADOWS AND COMPLEX STRUCTURES ON 4-MANIFOLDS." Journal of Knot Theory and Its Ramifications 17, no. 11 (2008): 1429–54. http://dx.doi.org/10.1142/s0218216508006683.

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We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and of Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spinc-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-dimensional handlebody is homotopic to a complex one.
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Brown, Lawrence G., and Hyun Ho Lee. "Homotopy Classification of Projections in the Corona Algebra of a Non-simple C*-algebra." Canadian Journal of Mathematics 64, no. 4 (2012): 755–77. http://dx.doi.org/10.4153/cjm-2011-092-x.

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AbstractWe study projections in the corona algebra of C(X) ⊗ K, where K is the C*-algebra of compact operators on a separable infinite dimensional Hilbert space and X = [0, 1], [0,∞), (−∞,∞), or [0, 1]/﹛0, 1﹜. Using BDF's essential codimension, we determine conditions for a projection in the corona algebra to be liftable to a projection in the multiplier algebra. We also determine the conditions for two projections to be equal in K0, Murray-von Neumann equivalent, unitarily equivalent, or homotopic. In light of these characterizations, we construct examples showing that the equivalence notions
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FIEDLER, THOMAS, and ARNAUD MORTIER. "ON HOMOTOPIES WITH TRIPLE POINTS OF CLASSICAL KNOTS." Journal of Knot Theory and Its Ramifications 21, no. 04 (2012): 1250038. http://dx.doi.org/10.1142/s0218216511009911.

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We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point p of the cylinder is called coherent if all three branches intersect at p pairwise with the same intersection index. A triple unknotting of a classical knot K is a homotopy which connects K with the trivial knot and which has as singularities only coherent triple points. We give a new formula for the first Vassiliev invariant v2(K) by using triple unknottings. As a corollary we obtain a very simple proof of the fact that passing a coherent triple point always changes the knot type. As another corollary we show that
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NIKKUNI, RYO. "EDGE-HOMOTOPY CLASSIFICATION OF SPATIAL COMPLETE GRAPHS ON FOUR VERTICES." Journal of Knot Theory and Its Ramifications 13, no. 06 (2004): 763–77. http://dx.doi.org/10.1142/s0218216504003433.

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Two spatial embeddings of a graph are said to be edge-homotopic if they are transformed into each other by self-crossing changes and ambient isotopies. We show that two spatial embeddings of the complete graph on four vertices are edge-homotopic if and only if they have the same α-invariant.
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NEHANIV, CHRYSTOPHER LEV. "ALGEBRAIC CONNECTIVITY." International Journal of Algebra and Computation 01, no. 04 (1991): 445–71. http://dx.doi.org/10.1142/s0218196791000316.

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Let [Formula: see text] be a type of algebra in the sense of universal algebra. By defining singular simplices in algebras and emulating singular [co] homology, we introduce for each variety, pseudo-variety, and divisional class V of type [Formula: see text], a homology and cohomology theory which measure the V-connectivity of type-[Formula: see text] algebras. Intuitively, if we were to think of an algebra as a space and subalgebras which lie in V as simplices, then V-connectivity describes the failure of subalgebras to lie in V, i.e., it describes the "holes" in this space. These [co]homolog
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Macías-Virgós, E., and D. Mosquera-Lois. "Homotopic distance between functors." Journal of Homotopy and Related Structures 15, no. 3-4 (2020): 537–55. http://dx.doi.org/10.1007/s40062-020-00269-x.

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Dissertations / Theses on the topic "Homotopic algebra"

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Cirici, Joana. "Homotopical Aspects of Mixed Hodge Theory." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/108950.

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In the present work, we analyse the categories of mixed Hodge complexes and mixed Hodge diagrams of differential graded algebras in these two directions: we prove the existence of both a Cartan-Eilenberg structure, via the construction of cofibrant minimal models, and a cohomological descent structure. This allows to interpret the results of Deligne, Beilinson, Morgan and Navarro within a common homotopical framework. In the additive context of mixed Hodge complexes we recover Beilinson's results. In our study we go a little further and show that the homotopy category of mixed Hodge complex
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Quemel, Taísa Fernanda de Lima. "Homotopia e aplicações /." São José do Rio Preto, 2016. http://hdl.handle.net/11449/136229.

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Orientador: João Peres Vieira<br>Banca: Eliris Cristina Rizziolli<br>Banca: Edivaldo Lopes dos Santos<br>Resumo: O objetivo deste trabalho é mostrar que πn(X) é sempre abeliano quando n ≥ 2 e que π1(X) é abeliano quando X for um H-espaço e por fim calcular alguns grupos de homotopia utilizando sequência exata de uma fibração<br>Abstract: The goal of this work is to show that πn(X) is always abelian when n ≥ 2 and that π1(X) is abelian when X is an H-space and finally calculate some homotopy groups using the exact sequence of a fibration<br>Mestre
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Robert-Nicoud, Daniel. "Opérades et espaces de Maurer-Cartan." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCD048.

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Cette thèse s’inscrit dans les thèmes de la théorie des opérades et de l’algèbre homotopique. Soient donnés un type d'algèbre, un type de cogèbres et une relation entre ces types de structures algébriques (codés respectivement par une opérade, une coopérade et un morphisme tordant). Il est possible alors de mettre une structure naturelle d’algèbre de Lie à homotopie près sur l’espace des applications linéaires d’une cogèbre C vers une algèbre A. On appelle l’algèbre de Lie `a homotopie près obtenue de cette fac¸on l’algèbre de convolution de A et C. Dans cette thèse, on étudie la théorie des a
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Hoefel, Eduardo Outeiral Correa. "Espaço de configurações e OCHA." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307207.

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Orientador: Alcibiades Rigas, Tomas Edson Barros<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-06T01:35:44Z (GMT). No. of bitstreams: 1 Hoefel_EduardoOuteiralCorrea_D.pdf: 1956293 bytes, checksum: 425e3f8509c6c6d5b7e71d692027dfaf (MD5) Previous issue date: 2006<br>Resumo: Esta tese consiste do estudo das OCHAs (Open-Closed Homotopy Algebras) sob os pontos de vista algébrico e geométrico. São demonstrados essencialmente dois resultados novos. O primeiro refere-se à definição de OCHA
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Pinzon, Daniel F. "VERTEX ALGEBRAS AND STRONGLY HOMOTOPY LIE ALGEBRAS." UKnowledge, 2006. http://uknowledge.uky.edu/gradschool_diss/382.

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Vertex algebras and strongly homotopy Lie algebras (SHLA) are extensively used in qunatum field theory and string theory. Recently, it was shown that a Courant algebroid can be naturally lifted to a SHLA. The 0-product in the de Rham chiral algebra has an identical formula to the Courant bracket of vector fields and 1-forms. We show that in general, a vertex algebra has an SHLA structure and that the de Rham chiral algebra has a non-zero l4 homotopy.
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Cagne, Pierre. "Towards a homotopical algebra of dependent types." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC063/document.

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Cette thèse est consacrée à l'étude des interactions entre les structures homotopiques en théorie des catégories et les modèles catégoriques de la théorie des types de Martin-Löf. Le mémoire s'articule selon trois axes: les bifibrationos de Quillen, les catégories homotopiques des bifibrations de Quillen, et les tribus généralisées. Le premier axe définit une nouvelle notion de bifibration classifiant les pseudo foncteurs avec de bonnes propriétés depuis un catégorie de modèles et à valeurs dans la 2-catégorie des catégories de modèles et adjonctions de Quillen entre elles. En particulier on m
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Rodríguez, Ordóñez Hugo. "Topological study of nonsingular bilinear maps /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1251841791&sid=5&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2006.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves - ). Also available for download via the World Wide Web; free to University of Oregon users.
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Sutton, Thomas. "Rational homotopy theory and derived commutative algebra." Thesis, University of Sheffield, 2016. http://etheses.whiterose.ac.uk/17667/.

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This thesis presents work relating to the rich connections between Rational Homotopy Theory and Commutative Algebra, and builds on the classical work of Quillen and Sullivan, and more recent work of Greenlees, Hess and Shamir.
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Driver, Maria Sosonkina Jr. "Parallel Sparse Linear Algebra for Homotopy Methods." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30718.

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Globally convergent homotopy methods are used to solve difficult nonlinear systems of equations by tracking the zero curve of a homotopy map. Homotopy curve tracking involves solving a sequence of linear systems, which often vary greatly in difficulty. In this research, a popular iterative solution tool, GMRES(k), is adapted to deal with the sequence of such systems. The proposed adaptive strategy of GMRES(k) allows tuning of the restart parameter k based on the GMRES convergence rate for the given problem. Adaptive GMRES(k) is shown to be superior to several other iterative techniques on anal
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Balchin, Scott Lewis. "Augmented homotopical algebraic geometry." Thesis, University of Leicester, 2017. http://hdl.handle.net/2381/40623.

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In this thesis we are interested in extending the theory of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. We introduce the concept of augmentation categories, which are a class of generalised Reedy categories. An augmentation category is a category which has enough structure that we can mirror the simplicial constructions which make up the theory of homotopical algebraic geometry. In particular, we construct a Quillen model structure on their presheaf categories, and introduce the concept of augmented hypercovers to define a local model str
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Books on the topic "Homotopic algebra"

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1966-, Vezzosi Gabriele, ed. Homotopical algebraic geometry II: Geometric stacks and applications. American Mathematical Society, 2008.

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Baues, Hans J. Algebraic homotopy. Cambridge University Press, 1989.

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Modern classical homotopy theory. American Mathematical Society, 2011.

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Stable homotopy over the Steenrod algebra. American Mathematical Society, 2001.

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Avramov, Luchezar L., J. Daniel Christensen, William G. Dwyer, Michael A. Mandell, and Brooke E. Shipley, eds. Interactions between Homotopy Theory and Algebra. American Mathematical Society, 2007. http://dx.doi.org/10.1090/conm/436.

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Østvær, Paul Arne. Homotopy Theory of C*-Algebras. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0565-6.

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Díaz, F. J. Díaz. Homotopía algebraica: Descripción e interrelación de las principales teorías. Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, 1994.

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Meyer, Jean-Pierre, Jack Morava, and W. Stephen Wilson, eds. Homotopy Invariant Algebraic Structures. American Mathematical Society, 1999. http://dx.doi.org/10.1090/conm/239.

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Felix, Yves, ed. Algebraic Topology Rational Homotopy. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0077790.

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Félix, Y. Rational Homotopy Theory. Springer New York, 2001.

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Book chapters on the topic "Homotopic algebra"

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Gelfand, Sergei I., and Yuri I. Manin. "Introduction to Homotopic Algebra." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-12492-5_5.

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Gelfand, Sergei I., and Yuri I. Manin. "Introduction to Homotopic Algebra." In Methods of Homological Algebra. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-03220-6_5.

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Paugam, Frédéric. "Homotopical Algebra." In Towards the Mathematics of Quantum Field Theory. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04564-1_9.

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Chen, Kuo-Tsai. "Homotopy of Algebras." In Collected Papers of K.-T. Chen. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-2096-1_28.

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Loday, Jean-Louis, and Bruno Vallette. "Homotopy Operadic Algebras." In Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30362-3_10.

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Voronov, Alexander A. "Homotopy Gerstenhaber algebras." In Conférence Moshé Flato 1999. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-1276-3_23.

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Hinich, V. A., and V. V. Schechtman. "On homotopy limit of homotopy algebras." In K-Theory, Arithmetic and Geometry. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078370.

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Lauder, Alan G. B. "Homotopy Methods for Equations over Finite Fields." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44828-4_3.

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Dubois-Violette, Michel, and Todor Popov. "Homotopy Commutative Algebra and 2-Nilpotent Lie Algebra." In Springer Proceedings in Mathematics & Statistics. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-55361-5_5.

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Aubry, Marc. "Attaching Cells in Topology and Algebra." In Homotopy Theory and Models. Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9086-1_6.

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Conference papers on the topic "Homotopic algebra"

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Kajiura, Hiroshige, and Jim Stasheff. "Homotopy algebra of open–closed strings." In Groups, homotopy and configuration spaces, in honour of Fred Cohen's 60th birthday. Mathematical Sciences Publishers, 2008. http://dx.doi.org/10.2140/gtm.2008.13.229.

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Hess, Kathryn. "Homotopic Hopf–Galois extensions: Foundations and examples." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.79.

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Borghesi, Simone. "Cohomology operations and algebraic geometry." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.75.

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Kadeishvili, Tornike. "Cohomology C∞-algebra and rational homotopy type." In Algebraic Topology - Old and New. Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc85-0-16.

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Golasiński, Marek, Daciberg L. Gonçalves, and Peter N. Wong. "A note on generalized equivariant homotopy groups." In Algebraic Topology - Old and New. Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc85-0-12.

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Saemann, Christian, Branislav Jurco, Hyungrok Kim, Tommaso Macrelli, and Martin Wolf. "Perturbative Quantum Field Theory and Homotopy Algebras." In Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity". Sissa Medialab, 2020. http://dx.doi.org/10.22323/1.376.0199.

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Sojakova, Kristina. "Higher Inductive Types as Homotopy-Initial Algebras." In POPL '15: The 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, 2015. http://dx.doi.org/10.1145/2676726.2676983.

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Priddy, Stewart. "Lectures on the stable homotopy of BG." In School and Conference in Algebraic Topology. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.11.289.

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Koschorke, Ulrich. "Some homotopy theoretical questions arising in Nielsen coincidence theory." In Algebraic Topology - Old and New. Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc85-0-18.

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Bodirsky, Manuel, Peter Jonsson, Barnaby Martin, and Antoine Mottet. "Classification Transfer for Qualitative Reasoning Problems." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/175.

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We study formalisms for temporal and spatial reasoning in the modern context of Constraint Satisfaction Problems (CSPs). We show how questions on the complexity of their subclasses can be solved using existing results via the powerful use of primitive positive (pp) interpretations and pp-homotopy. We demonstrate the methodology by giving a full complexity classification of all constraint languages that are first-order definable in Allen's Interval Algebra and contain the basic relations (s) and (f). In the case of the Rectangle Algebra we answer in the affirmative the old open question as to w
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