Cohomogeneity one Alexandrov spaces in low dimensions

Galaz-García, Fernando; Zarei, Masoumeh

Abstract

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.

Citation

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