2009/10/27 by Fernando Galaz‐García, Fernando Galaz-Garcia, Galaz-Garcia, Fernando +2
Mathematics · #51M25 #53C20 (Primary) #57S25 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Metric Geometry (math.MG) #math.DG #math.MG #msc:51M25 #msc:53C20 #msc:57S25
paper · pdf · doi:10.48550/arxiv.0910.5207
15 pages; Proposition 2.2 in v1 (now Proposition 4) has been modified. An omission in the classification of cohomogeneity one 4-manifolds was corrected
openalex publication_date 2009/10/27 · arxiv created 2010/09/19 · arxiv updated 2010/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.