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Cohomogeneity one Alexandrov spaces in low dimensions

Galaz-García, Fernando; Zarei, Masoumeh

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Authors

Masoumeh Zarei



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

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http://creativecommons.org/licenses/by/4.0/

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Advance online version This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.




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