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 one- and two-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 \( \mathbb{R}{P^2} \), which is not a manifold.
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This author was supported in part by CONACYT project #SEP-82471.
This author was supported in part by CONACYT Project #SEP-CO1-46274, CONACYT project #SEP-82471, and UNAM DGAPA project IN-115408.
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Galaz-Garcia, F., Searle, C. Cohomogeneity one Alexandrov spaces. Transformation Groups 16, 91–107 (2011). https://doi.org/10.1007/s00031-011-9122-0
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DOI: https://doi.org/10.1007/s00031-011-9122-0