Geodesic
Constructing geometrically equivalent hyperbolic orbifolds
McReynolds, David1 ; Meyer, Jeffrey2 ; Stover, Matthew3
1Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, United States
2Department of Mathematics, California State University, San Bernardino, 5500 University Parkway, San Bernardino, CA 92407-2318, United States
3Department of Mathematics, Temple University, 1805 N Broad St., Philadelphia, PA 19122, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 831-846
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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.

DOI : 10.2140/agt.2017.17.831
Classification : 51M10, 58J53, 11F06
Keywords: arithmetic lattices, hyperbolic manifolds, totally geodesic submanifolds

McReynolds, David  1   ; Meyer, Jeffrey  2   ; Stover, Matthew  3

1 Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, United States
2 Department of Mathematics, California State University, San Bernardino, 5500 University Parkway, San Bernardino, CA 92407-2318, United States
3 Department of Mathematics, Temple University, 1805 N Broad St., Philadelphia, PA 19122, United States 
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McReynolds, David; Meyer, Jeffrey; Stover, Matthew. Constructing geometrically equivalent hyperbolic orbifolds. Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 831-846. doi: 10.2140/agt.2017.17.831

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