group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group...
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in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space...
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In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of...
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mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients...
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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...
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In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking...
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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...
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mathematics, especially in the areas of abstract algebra dealing with group cohomology or relative homological algebra, Shapiro's lemma, also known as the...
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Tate cohomology groups are a slightly modified form of the usual cohomology groups of a finite group that combine homology and cohomology groups into...
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Eichler–Shimura isomorphism (redirect from Eichler cohomology)
mathematics, Eichler cohomology (also called parabolic cohomology or cuspidal cohomology) is a cohomology theory for Fuchsian groups, introduced by Eichler (1957)...
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Lyndon–Hochschild–Serre spectral sequence (category Group theory)
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...
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equivariant cohomology (or Borel cohomology) is a cohomology theory from algebraic topology which applies to topological spaces with a group action. It...
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In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological...
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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...
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some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW...
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mathematics, a nonabelian cohomology is any cohomology with coefficients in a nonabelian group, a sheaf of nonabelian groups or even in a topological space...
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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...
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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...
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Cyclic homology (redirect from Cyclic cohomology)
geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize...
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Derived functor (section Homology and cohomology)
{Ab}}^{op}} . Various notions of cohomology are special cases of Ext functors and therefore also derived functors. Group cohomology is the right derived functor...
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Ext functor (redirect from Ext group)
topology are used to define invariants of algebraic structures. The cohomology of groups, Lie algebras, and associative algebras can all be defined in terms...
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Homology (mathematics) (redirect from Homology group)
notion of the cohomology of a cochain complex, giving rise to various cohomology theories, in addition to the notion of the cohomology of a topological...
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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...
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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...
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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...
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Hilbert's Theorem 90 (section Cohomology)
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 (...
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and affine algebraic groups are group objects in the category of affine algebraic varieties. Such as group cohomology or equivariant K-theory. In particular...
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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...
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Projective representation (category Group theory)
perfect group there is a single universal perfect central extension of G that can be used. The analysis of the lifting question involves group cohomology. Indeed...
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class field theory using techniques of group cohomology applied to the idele class group and Galois cohomology. This treatment made more transparent some...
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