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 |
|---|---|
| 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 |
| Date of Publication (online): | 2021/02/21 |
| Year of first Publication: | 2019 |
| Publishing Institution: | Universität Augsburg |
| 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 |
