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, T=(S^1)^n, with free equivariant cohomology over the cohomology of BT. Here we characterise those finite T-CW complexes with connected isotropy groups for which an analogous result holds with integral coefficients.