integral homology

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• 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 make statements without some number of exceptional… …   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

• Abelian integral — In mathematics, an abelian integral in Riemann surface theory is a function related to the indefinite integral of a differential of the first kind. Suppose we are given a Riemann surface S and on it a differential 1 form ω that is everywhere… …   Wikipedia

• Casson invariant — In 3 dimensional topology, a part of the mathematical field of geometric topology, the Casson invariant is an integer valued invariant of oriented integral homology 3 spheres, introduced by Andrew Casson.Kevin Walker (1992) found an extension to… …   Wikipedia

• Schur multiplier — In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group of a group G. It was introduced by Issai Schur (1904) in his work on projective representations. Contents 1 Examples and properties 2 Re …   Wikipedia

• Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

• Universal coefficient theorem — In mathematics, the universal coefficient theorem in algebraic topology establishes the relationship in homology theory between the integral homology of a topological space X, and its homology with coefficients in any abelian group A. It states… …   Wikipedia

• Covering groups of the alternating and symmetric groups — In the mathematical area of group theory, the covering groups of the alternating and symmetric groups are groups that are used to understand the projective representations of the alternating and symmetric groups. The covering groups were… …   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

• Algebraic topology — is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situations this is too much to hope for… …   Wikipedia

• Acyclic space — In mathematics, an acyclic space is a topological space X in which cycles are always boundaries, in the sense of homology theory. This implies that the integral homology groups in all dimensions of X are isomorphic to the corresponding homology… …   Wikipedia