Cohomogeneity One Alexandrov Spaces

Details Cohomogeneity One Alexandrov Spaces Cohomogeneity One Alexandrov Spaces

2009-10-27

arxiv.org/abs/0910.5207v2

Mathematics

Differential Geometry

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

Scientific paper

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 $RP^2$, which is not a manifold.

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