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n-dimensional homology functor

См. также в других словарях:

  • 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

  • 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

  • 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

  • Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   Wikipedia

  • Cobordism — A cobordism (W;M,N). In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold. Two manifolds are cobordant if their disjoint… …   Wikipedia

  • Fundamental group — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of …   Wikipedia

  • Category theory — In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects and morphisms . Categories now appear in most branches of mathematics and in… …   Wikipedia

  • Natural transformation — This article is about natural transformations in category theory. For the natural competence of bacteria to take up foreign DNA, see Transformation (genetics). In category theory, a branch of mathematics, a natural transformation provides a way… …   Wikipedia

  • Duality (mathematics) — In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one to one fashion, often (but not always) by means of an involution operation: if the dual… …   Wikipedia

  • Categories of manifolds — In mathematics, specifically geometry and topology, there are many different notions of manifold, with more or less structure, and corresponding notions of map between manifolds , each of which yields a different category and its own… …   Wikipedia

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