Cohomogeneity One Alexandrov Spaces

Abstract

We obtain a structure theorem for closed, cohomogeneity one Alexandrov spaces and we classify closed, cohomogeneity one Alexandrov spaces in dimensions 3 and 4. As a corollary, we obtain the classification of closed, $n$-dimensional, cohomogeneity one Alexandrov spaces admitting an isometric $T^{n-1}$ action. In contrast to the 1- and 2-dimensional cases, where it is known that an Alexandrov space is a topological manifold, in dimension 3 the classification contains, in addition to the known cohomogeneity one manifolds, the spherical suspension of $R{P}^2$, which is not a manifold.

15 pages; Proposition 2.2 in v1 (now Proposition 4) has been modified. An omission in the classification of cohomogeneity one 4-manifolds was corrected

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Classification of Cohomogeneity One Manifolds in Low Dimensions
• Volume collapsed three-manifolds with a lower curvature bound