Equivariant cohomology of cohomogeneity-one actions: The topological case

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⁎(BG)-module structure is Cohen-Macaulay. The proof relies on the structure theorem for these actions recently obtained by Galaz-García and Zarei. We generalize in this way our previous result concerning smooth actions.