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Equivariant cohomology of cohomogeneity one actions: the topological case (1609.07316v2)
Published 23 Sep 2016 in math.AT
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 $H*(BG)$-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.