Exact cohomology sequences with integral coefficients for torus actions

Abstract

Using methods applied by Atiyah in equivariant K-theory, Bredon obtained exact sequences for the relative cohomologies (with rational coefficients) of the equivariant skeletons of (sufficiently nice) T-spaces X, $T=(S^1)^n,$ with free equivariant cohomology $H_T^*(X;{\mathbb Q})$ over $H_T^*({\rm pt};{\mathbb Q})=H^*(BT;{\mathbb Q}).$ Here we characterise those finite T-CW complexes with connected isotropy groups for which an analogous result holds with integral coefficients.