Invariants under deformation of the actions of topological groups

2016/05/20 by Viña, Andrés
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.06266

Abstract

Let φ and φ' be two homotopic actions of the topological group G on the topological space X. To an object A in the G-equivariant derived category D_φ(X) of X relative to the action φ we associate an object A' of category D_φ'(X), such that the corresponding G-equivariant compactly supported cohomologies H_G,c(X, A) and H_G,c(X, A') are isomorphic. When G is a Lie group and X is a subanalytic space, we prove that the G-equivariant cohomologies H_G(X, A) and H_G(X, A') are also isomorphic.

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