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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.

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Verlagsausgabe §
DOI: 10.5445/IR/1000122717
Veröffentlicht am 17.08.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 09.2020
Sprache Englisch
Identifikator ISSN: 0232-704X, 1572-9060
KITopen-ID: 1000122717
Erschienen in Annals of global analysis and geometry
Verlag Springer
Band 58
Heft 2
Seiten 109–146
Vorab online veröffentlicht am 07.07.2020
Nachgewiesen in Dimensions
Web of Science
Scopus
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