Combinatorial homology in a perspective of image analysis.
Grandis, Marco (2003)
Georgian Mathematical Journal
Similarity:
Grandis, Marco (2003)
Georgian Mathematical Journal
Similarity:
Jaroslav Guričan (1992)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
Homology functor in the spirit of the AST is defined, its basic properties are studied. Eilenberg-Steenrod axioms for this functor are formulated and established.
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 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...
Pitsch, Wolfgang, Scherer, Jérôme (2004)
Homology, Homotopy and Applications
Similarity:
Levine, Jerome (2001)
Algebraic & Geometric Topology
Similarity:
M. V. Mielke (1993)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the interval based homotopies and, for toposes, the excisions represented by “cutting out” subobjects....
Fred Richman (1976)
Fundamenta Mathematicae
Similarity:
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...