Homology sphere
Homology sphere In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some ... is simply connected, only that its fundamental group is perfect (see Hurewicz theorem). A rational homology sphere is defined similarly but we ...
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Fundamental group
Fundamental group In mathematics, the fundamental group is one of the basic concepts of ... a topological space there is a fundamental group that conveys information about the 1-dimensional ... space surrounding the given point. The fundamental group is the first homotopy group. Intuition and definition Before giving a ...
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Homology (mathematics)
Homology (mathematics) In mathematics (especially algebraic topology and abstract algebra), homology (in Greek homos = identical) is a certain ... such as a topological space or a group). See homology theory for more background. For a topological space, the homology groups are generally much easier to ...
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Reduced homology
Reduced homology In mathematics, reduced homology is a minor modification made to homology theory in algebraic topology, designed to make a point have all its homology groups zero. This change is required to ... then with the usual definitions the integral homology group H 0 (P) is an ...
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K-homology
K-homology In mathematics, K-homology is a homology theory on the category of compact Hausdorff ... homotopies. The $K^0(A)$ group is the abelian group of equivalence classes of even Fredholm ...
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Singular homology
Singular homology In algebraic topology, singular homology refers to the usual homology functor from the category of topological spaces ... the category of graded abelian groups and group homomorphisms. The homology of a space X is usually ...
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Homology theory
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 intuitive level homology is taken to be an equivalence ...
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Homology (sociology)
Homology (sociology) Homologies are a "structural 'resonances'...between ... to hang on to the notion of homology in a qualified sense. For it seems ... easily articulated to the interests of one group than are some others; similarly, that they ... easily articulated to the interests of one group than to those of another. This is ...
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Group theory
Group theory Group theory is that branch of mathematics concerned ... groups. Please refer to the Glossary of group theory for the definitions of terms used throughout group theory. See also list of group theory topics. History There are three ...
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Cyclic homology
Cyclic homology In mathematics, cyclic homology is an aspect of homological algebra. It ... such as a topological space or a group). See also Homology Homology theory External links A personal note ...
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