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Cohomology is an invariant of a topological space, formally "dual" to homology, and so it detects "holes" in a space. Cohomology has more algebraic structure than homology, ...

A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

The direct limit of the cohomology groups with coefficients in an Abelian group of certain coverings of a topological space.

An extension of a group H by a group N is a group G with a normal subgroup M such that M=N and G/M=H. This information can be encoded into a short exact sequence of groups ...

Exotic cohomology is a cohomology theory that extends index theory to a larger class of manifolds.

A group that has a primitive group action.

A fundamental result of de Rham cohomology is that the kth de Rham cohomology vector space of a manifold M is canonically isomorphic to the Alexander-Spanier cohomology ...

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

A finite group L is quasisimple if L=[L,L] and L/Z(L) is a simple group.

X is a p^'-group if p does not divide the group order of X.