Equivariant Alexandrov Geometry and Orbifold Finiteness

Harvey, John ORCID: https://orcid.org/0000-0001-9211-0060 2016. Equivariant Alexandrov Geometry and Orbifold Finiteness. Journal of Geometric Analysis 26 (3) , pp. 1925-1945. 10.1007/s12220-015-9614-6

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Abstract

Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If the sequence of actions is equicontinuous and converges in the equivariant Gromov–Hausdorff topology, then the limit space is equivariantly homeomorphic to spaces in the tail of the sequence. As a consequence, the class of Riemannian orbifolds of dimension n defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian orbifolds with a lower bound on the sectional curvature is finite up to orbifold homeomorphism.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer
ISSN:	1050-6926
Last Modified:	10 Nov 2022 11:33
URI:	https://orca.cardiff.ac.uk/id/eprint/150994

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