Classification of simply connected cohomogeneity one manifolds in lower dimensions

Abstract

A cohomogeneity one manifold is a topological manifold with an effective topological action of a compact Lie group whose quotient is one dimensional. Cohomogeneity one manifolds were introduced by Mostert in 1957, however Mostert's original structure theorem had two omissions. The first omission was corrected by Neumann in 1967 but the second omission was not corrected until 2015 by Galaz-Garcia and Zarei. In this paper we will examine the revised structure theorems for cohomogeneity one manifolds and compile all work done by Parker, Neumann, Mostert, Hoelscher, Galaz-Garcia and Zarei on the equivariant classification of closed, simply connected cohomogeneity one manifolds in dimensions up to 7.