compact homology

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• Homology manifold — In mathematics, a homology manifold (or generalized manifold)is a locally compact topological space X that looks locally like a topological manifold from the point of view of homology theory.DefinitionA homology G manifold (without boundary) of… …   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

• 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 regions — regions of immunoglobulin heavy and light chains containing about 110 amino acid residues and forming compact globular domains stabilized by one intrachain disulfide bond; they have a high degree of sequence homology and similar three dimensional …   Medical dictionary

• Morse homology — In mathematics, specifically in the field of differential topology, Morse homology is a homology theory defined for any smooth manifold. It is constructed using the smooth structure and an auxiliary metric on the manifold, but turns out to be… …   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

• Compactly-supported homology — In mathematics, a homology theory in algebraic topology is compactly supported if, in every degree n, the relative homology group Hn(X, A) of every pair of spaces (X, A) is naturally isomorphic to the direct limit of the nth relative homology… …   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

• Floer homology — is a mathematical tool used in the study of symplectic geometry and low dimensional topology. First introduced by Andreas Floer in his proof of the Arnold conjecture in symplectic geometry, Floer homology is a novel homology theory arising as an… …   Wikipedia

• Cohomology with compact support — In mathematics, cohomology with compact support refers to certain cohomology theories, usually with some condition requiring that cocycles should have compact support. de Rham cohomology with compact support for smooth manifolds Given a manifold… …   Wikipedia

• K-homology — In mathematics, K homology is a homology theory on the category of compact Hausdorff spaces. It classifies the elliptic pseudo differential operators acting on the vector bundles over a space. In terms of C^* algebras, it classifies the Fredholm… …   Wikipedia