Fernando Galaz-García fernando.galaz-garcia@durham.ac.uk
Associate Professor
Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with one-dimensional orbit space, they are said to be of cohomogeneity one. Well-known examples include cohomogeneity-one Riemannian manifolds with a uniform lower sectional curvature bound; such spaces are of interest in the context of non-negative and positive sectional curvature. In the present article we classify closed, simply connected cohomogeneity-one Alexandrov spaces in dimensions 5, 6 and 7. This yields, in combination with previous results for manifolds and Alexandrov spaces, a complete classification of closed, simply connected cohomogeneity-one Alexandrov spaces in dimensions at most 7.
Galaz-García, F., & Zarei, M. (2020). Cohomogeneity one Alexandrov spaces in low dimensions. Annals of Global Analysis and Geometry, 58(2), 109-146. https://doi.org/10.1007/s10455-020-09716-7
Journal Article Type | Article |
---|---|
Acceptance Date | May 5, 2020 |
Online Publication Date | Jul 7, 2020 |
Publication Date | 2020-09 |
Deposit Date | Jul 22, 2020 |
Publicly Available Date | Jul 22, 2020 |
Journal | Annals of Global Analysis and Geometry |
Print ISSN | 0232-704X |
Electronic ISSN | 1572-9060 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 58 |
Issue | 2 |
Pages | 109-146 |
DOI | https://doi.org/10.1007/s10455-020-09716-7 |
Public URL | https://durham-repository.worktribe.com/output/1266028 |
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