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Cohomogeneity One Alexandrov Spaces. [Preprint]

Galaz-Garcia, Fernando; Searle, Catherine

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 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 RP2, which is not a manifold.


Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Buchaufsatz
Jahr 2009
Sprache Englisch
Identifikator KITopen ID: 1000051175
Erschienen in arXiv [math.DG]
Seiten arXiv:0910.5207
URLs http://arxiv.org/abs/0910.5207
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