Search results
Results From The WOW.Com Content Network
In mathematics, a nonabelian cohomology is any cohomology with coefficients in a nonabelian group, a sheaf of nonabelian groups or even in a topological space. If homology is thought of as the abelianization of homotopy (cf. Hurewicz theorem ), then the nonabelian cohomology may be thought of as a dual of homotopy groups .
In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette and Carlos Simpson) is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, projective complex algebraic variety, or a compact Kähler manifold.
Group cohomology plays a role in the investigation of fixed points of a group action in a module or space and the quotient module or space with respect to a group action. Group cohomology is used in the fields of abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper.
A presentation of class field theory in terms of group cohomology was carried out by Claude Chevalley, Emil Artin and others, mainly in the 1940s. This resulted in a formulation of the central results by means of the group cohomology of the idele class group.
Introduces most general nonabelian cohomology of ω-categories with ω-categories as coefficients when he realized that general cohomology is about coloring simplices in ω-categories. There are two methods of constructing general nonabelian cohomology, as nonabelian sheaf cohomology in terms of descent for ω-category valued sheaves, and in ...
Sheaf cohomology is a rich generalization of singular cohomology, allowing more general "coefficients" than simply an abelian group. For every sheaf of abelian groups E on a topological space X , one has cohomology groups H i ( X , E ) for integers i .
Non-abelian or nonabelian may refer to: Non-abelian group, in mathematics, a group that is not abelian ... Nonabelian cohomology, a cohomology; Abelian (disambiguation)
The question of what groups are extensions of by is called the extension problem, and has been studied heavily since the late nineteenth century.As to its motivation, consider that the composition series of a finite group is a finite sequence of subgroups {}, where each {+} is an extension of {} by some simple group.