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arXiv · 0910.5207

Cohomogeneity One Alexandrov Spaces

Fernando Galaz-Garcia·Catherine Searle
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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 $RP^2$, which is not a manifold.

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Fernando Galaz-Garcia, Catherine Searle. 2009-10-27. Cohomogeneity One Alexandrov Spaces. https://arxiv.org/abs/0910.5207

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