Cohomogeneity One Alexandrov Spaces. [Preprint]

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.