Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms

Jaroslav Guričan

Displaying similar documents to “Homology theory in the AST II. Basic concepts, Eilenberg-Steenrod's axioms”

Combinatorial homology in a perspective of image analysis.

Grandis, Marco (2003)

Georgian Mathematical Journal

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Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris

Jaroslav Guričan (1993)

Commentationes Mathematicae Universitatis Carolinae

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The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.

Effective homology for homotopy colimit and cofibrant replacement

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 $X : ℐ \to sSet$ 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...

Successive homology operations and their applications

Su-Cheng Chang (1966)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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