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Constructing geometrically equivalent hyperbolic orbifolds

David McReynolds, Jeffrey S Meyer and Matthew Stover

Algebraic & Geometric Topology 17 (2017) 831–846

We construct families of nonisometric hyperbolic orbifolds that contain the same isometry classes of nonflat totally geodesic subspaces. The main tool is a variant of the well-known Sunada method for constructing length-isospectral Riemannian manifolds that handles totally geodesic submanifolds of multiple codimensions simultaneously.

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arithmetic lattices, hyperbolic manifolds, totally geodesic submanifolds
Mathematical Subject Classification 2010
Primary: 51M10, 58J53
Secondary: 11F06
Received: 24 July 2015
Revised: 28 August 2016
Accepted: 8 September 2016
Published: 14 March 2017
David McReynolds
Department of Mathematics
Purdue University
150 N. University St.
West Lafayette, IN 47907
United States
Jeffrey S Meyer
Department of Mathematics
California State University, San Bernardino
5500 University Parkway
San Bernardino, CA 92407-2318
United States
Matthew Stover
Department of Mathematics
Temple University
1805 N Broad St.
Philadelphia, PA 19122
United States