Cohomogeneity one Alexandrov spaces in low dimensions

TL;DR

This paper classifies low-dimensional cohomogeneity-one Alexandrov spaces and demonstrates that certain orbifolds with cohomogeneity one actions are equivalent to smooth good orbifolds, advancing understanding of their structure.

Contribution

It provides a classification of closed, simply-connected cohomogeneity-one Alexandrov spaces in dimensions 5 to 7 and links these to smooth orbifolds with cohomogeneity one actions.

Findings

Classification of cohomogeneity-one Alexandrov spaces in dimensions 5, 6, and 7.

Every closed, simply-connected orbifold with a cohomogeneity one action is a smooth good orbifold.

Establishes a correspondence between Alexandrov spaces and smooth orbifolds in low dimensions.

Abstract

We classify closed, simply-connected cohomogeneity-one Alexandrov spaces in dimensions $5$, $6$ and $7$. We show that every closed, simply-connected smooth $n$-orbifold, $2\leq n\leq 7$ with a cohomogeneity one action is equivariantly homeomorphic to a smooth good orbifold of cohomogeneity one.