Seminar

Cohomogeneity one topological manifolds were introduced by Mostert in 1957. In this talk I will discuss the structure of these spaces and show that not every cohomogeneity one topological manifold is equivariantly homeomorphic to a smooth cohomogeneity one manifold. I will then discuss the classification of closed, simply connected cohomogeneity one topological manifolds in dimensions 5, 6, and 7. In these dimensions, these manifolds are homeomorphic to smooth manifolds. This fixes and old gap in the literature. Time permitting, I will also discuss how this class of manifolds relates to the more general class of cohomogeneity-one Alexandrov spaces. This is joint work with Masoumeh Zarei.