- simplicial homology
- мат. симплициальная гомология
Большой англо-русский и русско-английский словарь. 2001.
simplicial homology
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Simplicial homology — In mathematics, in the area of algebraic topology, simplicial homology is a theory with a finitary definition, and is probably the most tangible variant of homology theory. Simplicial homology concerns topological spaces whose building blocks are … Wikipedia
Homology (mathematics) — In mathematics (especially algebraic topology and abstract algebra), homology (in Greek ὁμός homos identical ) is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a… … Wikipedia
Homology theory — In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It can be broadly defined as the study of homology theories on topological spaces. Simple explanation At the… … Wikipedia
Homology sphere — In algebraic topology, a homology sphere is an n manifold X having the homology groups of an n sphere, for some integer n ≥ 1. That is, we have: H 0( X ,Z) = Z = H n ( X ,Z)and : H i ( X ,Z) = {0} for all other i .Therefore X is a connected space … Wikipedia
Simplicial set — In mathematics, a simplicial set is a construction in categorical homotopy theory which is a purely algebraic model of the notion of a well behaved topological space. Historically, this model arose from earlier work in combinatorial topology and… … Wikipedia
Simplicial complex — In mathematics, a simplicial complex is a topological space of a particular kind, constructed by gluing together points, line segments, triangles, and their n dimensional counterparts (see illustration). Simplicial complexes should not be… … Wikipedia
Simplicial approximation theorem — In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation) approximated by ones that are piecewise of the simplest kind. It applies… … Wikipedia
Pushforward (homology) — Let X and Y be two topological spaces and f:X ightarrow Y a continuous function. Then f induces a homomorphism between the homology groups f {*}:H nleft(X ight) ightarrow H nleft(Y ight) for ngeq0. We say that f {*} is the pushforward induced by… … Wikipedia
Borel-Moore homology — In mathematics, Borel Moore homology or homology with closed support is a homology theory for locally compact spaces. For compact spaces, the Borel Moore homology coincide with the usual singular homology, but for non compact spaces, it usually… … Wikipedia
Hochschild homology — In mathematics, Hochschild homology is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain functors. Definition of Hochschild homology of algebras Let k be a ring, A an associative k… … Wikipedia
Intersection homology — In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them… … Wikipedia
