Equivariant cohomology of cohomogeneity one actions: the topological case

Abstract

We show that for any cohomogeneity one continuous action of a compact connected Lie group $G$ on a closed topological manifold the equivariant cohomology equipped with its canonical $H^{\ast }(BG)$-module structure is Cohen-Macaulay. The proof relies on the structure theorem for these actions recently obtained by Galaz-Garcia and Zarei. We generalize in this way our previous result concerning smooth actions.

3 pages; final version, to appear in Topology Appl

References in corpus (1)

• Syzygies in equivariant cohomology for non-abelian Lie groups