Relevant bibliographies by topics / Homotopy coherence

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Homotopy coherence'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Homotopy coherence"

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Porter, Tim, and Jim Stasheff. "Homotopy Coherent Representations." Symmetry 14, no. 3 (2022): 553. http://dx.doi.org/10.3390/sym14030553.

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Homotopy coherence has a considerable history, albeit also by other names. For this volume highlighting symmetries, the appropriate use is homotopy coherence of representations, at one time known as representations up to homotopy/homotopy coherent representations. We present a brief semi-historical survey, providing some links that may not be common knowledge.
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Geoghegan, Ross, and Andrew Nicas. "Homotopy periodicity and coherence." Proceedings of the American Mathematical Society 124, no. 9 (1996): 2889–95. http://dx.doi.org/10.1090/s0002-9939-96-03543-5.

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Hardie, K. A., K. H. Kamps, and P. J. Witbooi. "A Note On Homotopy Pushout And Homotopy Coherence." Quaestiones Mathematicae 26, no. 4 (2003): 399–403. http://dx.doi.org/10.2989/16073600309486070.

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Yanofsky, Noson S. "Coherence, Homotopy and 2-Theories." K-Theory 23, no. 3 (2001): 203–35. http://dx.doi.org/10.1023/a:1011893700822.

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YALIN, SINAN. "Simplicial localisation of homotopy algebras over a prop." Mathematical Proceedings of the Cambridge Philosophical Society 157, no. 3 (2014): 457–68. http://dx.doi.org/10.1017/s0305004114000437.

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AbstractWe prove that a weak equivalence between two cofibrant (colored) props in chain complexes induces a Dwyer–Kan equivalence between the simplicial localisations of the associated categories of algebras. This homotopy invariance under base change implies that the homotopy category of homotopy algebras over a propPdoes not depend on the choice of a cofibrant resolution ofP, and gives thus a coherence to the notion of algebra up to homotopy in this setting. The result is established more generally for algebras in combinatorial monoidal dg categories.
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Dugger, Daniel. "Coherence for invertible objects and multigraded homotopy rings." Algebraic & Geometric Topology 14, no. 2 (2014): 1055–106. http://dx.doi.org/10.2140/agt.2014.14.1055.

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Kashiwabara, Takuji. "Mod p K-theory of Ω∞Σ∞X revisited". Mathematical Proceedings of the Cambridge Philosophical Society 114, № 2 (1993): 219–21. http://dx.doi.org/10.1017/s0305004100071553.

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In this note we present a new proof of a theorem of McClure on K*(Ω∞Σ∞X, Z/p) [11], in the special case when X is a finite complex with K1(X; Z/p) = 0. Although our method does not work in the full generality covered by his work, our argument requires neither a geometric interpretation of complex k-theory nor all the delicate coherence properties of its multiplication. Since BP-theory is not likely to possess such coherence properties [9], the possibility of generalizing his approach to the case of higher Morava K-theory does not seem feasible. On the contrary, the main ingredient of our appro
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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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Karar, Faten Ragab, Fatma Elzhraa Ahmed Mohammed, and A. A. El Fattah. "The excision theory for homology theory through A_∞-algebras." Edelweiss Applied Science and Technology 8, no. 6 (2024): 9472–86. https://doi.org/10.55214/25768484.v8i6.4026.

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This paper investigated A_∞-algebras, which are generalizations of associative algebras that incorporate higher homotopy structures. We began by revisiting the fundamental definitions and properties of A_∞-algebras and their associated homological theories, providing a solid foundation for understanding these complex structures. The study included an in-depth analysis of simplicial homology as it relates to A_∞-algebras, focusing on significant results, particularly those concerning excision theory. In this context, we introduced new insights into the relationship between bar homology and simp
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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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Dissertations / Theses on the topic "Homotopy coherence"

1

Ribeiro, Duarte Chambel. "Coherent presentation for the hypoplactic monoid of rank n." Master's thesis, 2017. http://hdl.handle.net/10362/23281.

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In this thesis, we construct a coherent presentation for the hypoplactic monoid of rank n and characterize the confluence diagrams associated with it, then we use the theory of quasi-Kashiwara operators and quasi-crystal graphs to prove that all confluence diagrams can be obtained from those diagrams whose vertices are highest-weight words. To do so, we first give a complete rewriting system for the hypoplactic monoid of rank n, then, using an extension of the Knuth–Bendix completion procedure called the homotopical completion procedure, we compute the previously mentioned coherent prese
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Book chapters on the topic "Homotopy coherence"

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Goerss, Paul G., and John F. Jardine. "Simplicial functors and homotopy coherence." In Simplicial Homotopy Theory. Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8707-6_9.

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Goerss, Paul G., and John F. Jardine. "Simplicial functors and homotopy coherence." In Simplicial Homotopy Theory. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-0346-0189-4_9.

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Schwänzl, R., and R. M. Vogt. "Coherence in homotopy group actions." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0072833.

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Mardešić, Sibe. "Coherent homotopy." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-13064-3_3.

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Mardešić, Sibe. "Coherent homotopy of sequences." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-13064-3_4.

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Mardešić, Sibe. "Coherent homotopy and localization." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-13064-3_5.

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Mardešić, Sibe. "Coherent homotopy as a Kleisli category." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-13064-3_6.

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Moerdijk, Ieke, and Bertrand Toën. "Boardman–Vogt resolution and homotopy coherent nerve." In Simplicial Methods for Operads and Algebraic Geometry. Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0348-0052-5_6.

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"Homotopy Coherence." In Abstract Homotopy and Simple Homotopy Theory. WORLD SCIENTIFIC, 1997. http://dx.doi.org/10.1142/9789812831989_0005.

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Hardie, K. A., and K. H. Kamps. "Coherent Homotopy over a Fixed Space." In Handbook of Algebraic Topology. Elsevier, 1995. http://dx.doi.org/10.1016/b978-044481779-2/50006-7.

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