Equivariant Simplicial Cohomology With Local Coefficients and its Classification

Abstract

We introduce equivariant twisted cohomology of a simplicial set equipped with simplicial action of a discrete group and prove that for suitable twisting function induced from a given equivariant local coefficients, the simplicial version of Bredon-Illman cohomology with local coefficients is isomorphic to equivariant twisted cohomology. The main aim of this paper is to prove a classification theorem for equivariant simplicial cohomology with local coefficients.

25 pages

Cited by in corpus (1)

• On a theorem of Eilenberg in simplicial Bredon-Illman cohomology with local coefficients