Cohomogeneity one topological manifolds revisited
Fernando Galaz-Garcia, Masoumeh Zarei

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 , , and and obtain topological characterizations of these spaces. In these dimensions, these manifolds are homeomorphic to smooth manifolds.
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