On the equivariant cohomology of cohomogeneity one Alexandrov spaces
- 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 Cohen-Macaulay. 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 Cohen-Macaulay. 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.
Author: | Manuel AmannGND, Masoumeh ZareiGND |
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Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/83636 |
URL: | https://arxiv.org/abs/1910.06309v2 |
Parent Title (English): | arXiv |
Type: | Preprint |
Language: | English |
Year of first Publication: | 2019 |
Release Date: | 2021/02/21 |
Issue: | arXiv:1910.06309 |
Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Differentialgeometrie |