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...

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

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

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...

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

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...

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...

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

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...

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

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

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

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

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...

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

algebra cohomology is a cohomology theory for Lie algebras. It was first introduced in 1929 by Élie Cartan to study the topology of Lie groups and homogeneous...

absolute Galois group. Its second cohomology group is isomorphic to the Brauer group of K (by Hilbert's theorem 90, its first cohomology group is zero). If...

a natural setting in which group cohomology lives. Furthermore, the above isomorphism suggests defining cohomology groups for negative values of n, and...

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

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

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

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

the cocycles in the second cohomology group in group cohomology. Suppose G is a group and A is an abelian group. For a group extension 1 → A → X → G →...

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 (...

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

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...

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...

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...