On the equivariant cohomology of cohomogeneity one Alexandrov spaces
Abstract
We give a characterization of those Alexandrov spaces admitting a cohomogeneity one action of a compact connected Lie group $G$ for which the action is CohenMacaulay. This generalizes a similar result for manifolds to the singular setting of Alexandrov spaces where, in contrast to the manifold case, we find several actions which are not CohenMacaulay. In fact, we present results in a slightly more general context. We extend the methods in this field by a conceptual approach on equivariant cohomology via rational homotopy theory using an explicit rational model for a double mapping cylinder.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.06309
 Bibcode:
 2019arXiv191006309A
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Algebraic Topology
 EPrint:
 Theorem A generalized, examples added to show it is sharp