# cohomology

﻿
cohomology
a) A theory associating a system of quotient groups to each topological space.
b) A system of quotient groups associated to a topological space.

Wikipedia foundation.

### Look at other dictionaries:

• 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 — noun Date: circa 1959 a part of the theory of topology in which groups are used to study the properties of topological spaces and which is related in a complementary way to homology theory called also cohomology theory • cohomological adjective …   New Collegiate Dictionary

• 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

• Cohomology with compact support — In mathematics, cohomology with compact support refers to certain cohomology theories, usually with some condition requiring that cocycles should have compact support. de Rham cohomology with compact support for smooth manifolds Given a manifold… …   Wikipedia

• 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 theory — noun see cohomology …   New Collegiate Dictionary

• 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

• 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

• 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