group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group...

in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space...

In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of...

mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients...

Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A...

Weyl groups to be simple algebraic groups over the field with one element. For a non-abelian connected compact Lie group G, the first group cohomology of...

mathematics, especially in the areas of abstract algebra dealing with group cohomology or relative homological algebra, Shapiro's lemma, also known as the...

Tate cohomology groups are a slightly modified form of the usual cohomology groups of a finite group that combine homology and cohomology groups into...

In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking...

sequence relating the group cohomology of a normal subgroup N and the quotient group G/N to the cohomology of the total group G. The spectral sequence...

discrete gauge theory. One can add additional twist terms allowed by group cohomology theory such as Dijkgraaf–Witten topological gauge theory. There are...

equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group action. It...

mathematics, a nonabelian cohomology is any cohomology with coefficients in a nonabelian group, a sheaf of nonabelian groups or even in a topological space...

mathematics, Eichler cohomology (also called parabolic cohomology or cuspidal cohomology) is a cohomology theory for Fuchsian groups, introduced by Eichler (1957)...

some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW...

In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological...

Motivic cohomology is an invariant of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the...

When X is a G-module, XG is the zeroth cohomology group of G with coefficients in X, and the higher cohomology groups are the derived functors of the functor...

{Ab}}^{op}} . Various notions of cohomology are special cases of Ext functors and therefore also derived functors. Group cohomology is the right derived functor...

group are a collection of properties that allow the use of various algebraic and topological tools, for example group cohomology, to study the group....

the Bohr compactification, and in group cohomology theory of Lie groups. A discrete isometry group is an isometry group such that for every point of the...

and affine algebraic groups are group objects in the category of affine algebraic varieties. Such as group cohomology or equivariant K-theory. In particular...

described by group theory. For bosonic SPT phases with pure gauge anomalous boundary, it was shown that they are classified by group cohomology theory: those...

topology are used to define invariants of algebraic structures. The cohomology of groups, Lie algebras, and associative algebras can all be defined in terms...

complex manifolds. Let M be a complex manifold. Then the Dolbeault cohomology groups H p , q ( M , C ) {\displaystyle H^{p,q}(M,\mathbb {C} )} depend on...

with arbitrary Galois group G = Gal(L/K), then the first cohomology group of G, with coefficients in the multiplicative group of L, is trivial: H 1 (...

2 ) {\displaystyle \omega \in H^{3}(B\pi _{1},\pi _{2})} a cohomology class. These groups can be encoded as homotopy 2 {\displaystyle 2} -types X {\displaystyle...

theory. This was first done by Emil Artin and Tate using the theory of group cohomology, and in particular by developing the notion of class formations. Later...

Kampen theorem for an example. An example is group cohomology of a group which equals the singular cohomology of its classifying space, see Weibel 1994, §8...

geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize...