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singular cohomology

См. также в других словарях:

  • 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

  • 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

  • Cohomology ring — In mathematics, specifically algebraic topology, the cohomology ring of a topological space X is a ring formed from the cohomology groups of X together with the cup product serving as the ring multiplication. Here cohomology is usually understood …   Wikipedia

  • Singular homology — In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of topological invariants of a topological space X , the so called homology groups H n(X). Singular homology is a particular example of 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

  • Sheaf cohomology — In mathematics, sheaf cohomology is the aspect of sheaf theory, concerned with sheaves of abelian groups, that applies homological algebra to make possible effective calculation of the global sections of a sheaf F. This is the main step, in… …   Wikipedia

  • De Rham cohomology — For Grothendieck s algebraic de Rham cohomology see Crystalline cohomology. In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic… …   Wikipedia

  • Čech cohomology — In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. Contents 1 Motivation 2… …   Wikipedia

  • Crystalline cohomology — In mathematics, crystalline cohomology is a Weil cohomology theory for schemes introduced by Alexander Grothendieck (1966, 1968) and developed by Pierre Berthelot (1974). Its values are modules over rings of Witt vectors over the base… …   Wikipedia

  • Deligne cohomology — In mathematics, Deligne cohomology is the hypercohomology of the Deligne complex of a complex manifold. It was introduced by Pierre Deligne in unpublished work in about 1972 as a cohomology theory for algebraic varieties that includes both… …   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

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