Cohomogeneity one topological manifolds revisited

TL;DR

This paper provides a corrected structure theorem for cohomogeneity one topological manifolds, completing their classification in dimensions 5 to 7 and establishing their homeomorphism to smooth manifolds.

Contribution

It corrects an oversight in the literature and completes the classification of simply connected cohomogeneity one topological manifolds in dimensions 5 to 7.

Findings

Complete classification of these manifolds in dimensions 5-7

Topological characterizations of the classified manifolds

Proof that these manifolds are homeomorphic to smooth manifolds

Abstract

We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply connected cohomogeneity one topological manifolds in dimensions $5$, $6$, and $7$ and obtain topological characterizations of these spaces. In these dimensions, these manifolds are homeomorphic to smooth manifolds.