cohomology group

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• Tate cohomology group — In mathematics, Tate cohomology groups are a slightly modified form of the usual cohomology groups of a finite group that combine homology and cohomology groups into one sequence. They were invented by John Tate, and are used in class field… …   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

• Cohomology — In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries.… …   Wikipedia

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• Group extension — In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence:1 ightarrow N… …   Wikipedia

• Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

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• Cohomology of algebras — In mathematics, the homology or cohomology of an algebra may refer to Banach algebra cohomology of a bimodule over a Banach algebra Cyclic homology of an associative algebra Group cohomology of a module over a group ring or a representation of a… …   Wikipedia

• Cohomology operation — In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape of the simple definition that if F is a functor defining a cohomology theory, then a… …   Wikipedia

• Étale cohomology — In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil… …   Wikipedia

• List of cohomology theories — This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at… …   Wikipedia