Displaying similar documents to “Foundations of Vietoris homology theory with applications to non-compact spaces”

Khovanov homology, its definitions and ramifications

Oleg Viro (2004)

Fundamenta Mathematicae

Similarity:

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...

Transverse Homology Groups

S. Dragotti, G. Magro, L. Parlato (2006)

Bollettino dell'Unione Matematica Italiana

Similarity:

We give, here, a geometric treatment of intersection homology theory.

Effective homology for homotopy colimit and cofibrant replacement

Marek Filakovský (2014)

Archivum Mathematicum

Similarity:

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 X : ℐ → sSet such that each simplicial set X ( i ) has effective homology, we present an algorithm computing the homotopy colimit hocolim X as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement X cof of X as a diagram with effective homology. This is applied to computing of equivariant cohomology...

On a homology of algebras with unit

Jacek Dębecki (2014)

Annales Polonici Mathematici

Similarity:

We present a very general construction of a chain complex for an arbitrary (even non-associative and non-commutative) algebra with unit and with any topology over a field with a suitable topology. We prove that for the algebra of smooth functions on a smooth manifold with the weak topology the homology vector spaces of this chain complex coincide with the classical singular homology groups of the manifold with real coefficients. We also show that for an associative and commutative algebra...

Homology of representable sets

Marian Mrozek, Bogdan Batko (2010)

Annales Polonici Mathematici

Similarity:

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.

On the first homology of Peano continua

Gregory R. Conner, Samuel M. Corson (2016)

Fundamenta Mathematicae

Similarity:

We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer...

A 2-category of chronological cobordisms and odd Khovanov homology

Krzysztof K. Putyra (2014)

Banach Center Publications

Similarity:

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...