Equivariant Simplicial Cohomology With Local Coefficients and its Classification

2009/05/14 by Mukherjee, Goutam, Sen, Debasis
#55N25 #55N91 #55R15 #55R91 #55U10 #57S99 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.0905.2279

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.

Related

• Equivariant Twisted Cartan Cohomology Theory
• On a theorem of Eilenberg in simplicial Bredon-Illman cohomology with local coefficients
• Twisted equivariant K-theory for proper actions of discrete groups
• Representing Bredon cohomology with local coefficients
• Steenrod's reduced power operations in simplicial Bredon-Illman cohomology with local coefficients