Volume 17, issue 1 (2013)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Periodic flats and group actions on locally symmetric spaces

Grigori Avramidi

Geometry & Topology 17 (2013) 311–327
Abstract

We use maximal periodic flats to show that on a finite volume irreducible locally symmetric manifold of dimension 3, no metric has more symmetry than the locally symmetric metric. We also show that if a finite volume metric is not locally symmetric, then its lift to the universal cover has discrete isometry group.

Keywords
aspherical manifolds, locally symmetric spaces, discontinuous transformation groups, smith theory
Mathematical Subject Classification 2010
Primary: 57S15, 57S20
References
Publication
Received: 1 August 2011
Revised: 10 October 2012
Accepted: 7 November 2012
Published: 8 March 2013
Proposed: Steve Ferry
Seconded: Walter Neumann, Jean-Pierre Otal
Authors
Grigori Avramidi
Department of Mathematics
University of Chicago
5734 S. University Avenue
Chicago, IL 60637
USA
http://math.uchicago.edu/~gavramid