homology theory

homology theory
noun see homology

New Collegiate Dictionary. 2001.

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  • 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

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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 — noun (plural gies) Date: circa 1656 1. a similarity often attributable to common origin 2. a. likeness in structure between parts of different organisms (as the wing of a bat and the human arm) due to evolutionary differentiation from a… …   New Collegiate Dictionary

  • Homology (anthropology) — In anthropology and archaeology, homology is a type of analogy whereby two human beliefs, practices or artefacts are separated by time but share similarities due to genetic or historical connections. Specifically in anthropology, a homology is a… …   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

  • 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

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  • Cyclic homology — In homological algebra, cyclic homology and cyclic cohomology are (co)homology theories for associative algebras introduced by Alain Connes around 1980, which play an important role in his noncommutative geometry. They were independently… …   Wikipedia

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