Homotopy and homology of finite lattices.
Blass, Andreas (2003)
The Electronic Journal of Combinatorics [electronic only]
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Blass, Andreas (2003)
The Electronic Journal of Combinatorics [electronic only]
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Björner, Anders, Wachs, Michelle L. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Yuzvinsky, Sergey (1999)
Publications de l'Institut Mathématique. Nouvelle Série
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Grandis, Marco (2003)
Georgian Mathematical Journal
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Bruns, Winfried, Vetter, Udo (1998)
Beiträge zur Algebra und Geometrie
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Pitsch, Wolfgang, Scherer, Jérôme (2004)
Homology, Homotopy and Applications
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S. K. Kaul (1970)
Colloquium Mathematicae
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S. Dragotti, G. Magro, L. Parlato (2006)
Bollettino dell'Unione Matematica Italiana
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We give, here, a geometric treatment of intersection homology theory.
Marek Filakovský (2014)
Archivum Mathematicum
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We extend the notion of simplicial set with effective homology presented in [22] to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets such that each simplicial set has effective homology, we present an algorithm computing the homotopy colimit as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement of as a diagram with effective homology. This is applied to computing of equivariant cohomology...
Marian Mrozek, Bogdan Batko (2010)
Annales Polonici Mathematici
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We generalize the notion of cubical homology to the class of locally compact representable sets in order to propose a new convenient method of reducing the complexity of a set while computing its homology.
Krzysztof K. Putyra (2014)
Banach Center Publications
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We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordisms and show that it is 2-commutative: the composition of 2-morphisms along any 3-dimensional subcube is trivial. This allows us to create a chain complex whose homotopy type modulo certain relations is a link invariant. Both the original and...
J. Dugundji (1966)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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A. Blanco, J. Majadas, A.G. Rodicio (1996)
Inventiones mathematicae
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Oleg Viro (2004)
Fundamenta Mathematicae
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Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups labelled by pairs of integers. These groups were constructed as the homology groups of certain chain complexes. The Euler characteristics of these complexes are the coefficients of the Jones polynomial of the link. The original construction is overloaded with algebraic details. Most of the specialists use adaptations of it stripped off the details. The goal of this paper is to overview these...
Daniel Krasner (2009)
Fundamenta Mathematicae
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We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl₃-homology.