Transformation Groups

, Volume 16, Issue 1, pp 91–107

Cohomogeneity one Alexandrov spaces

Article

DOI: 10.1007/s00031-011-9122-0

Cite this article as:
Galaz-Garcia, F. & Searle, C. Transformation Groups (2011) 16: 91. doi:10.1007/s00031-011-9122-0

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 Tn−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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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional, Autónoma de MéxicoCuernavacaMexico
  2. 2.Mathematisches Institut, WWUMünsterGermany

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