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Totally geodesic spectra of arithmetic hyperbolic spaces


Author: Jeffrey S. Meyer
Journal: Trans. Amer. Math. Soc. 369 (2017), 7549-7588
MSC (2010): Primary 11E12, 11F06, 20H10, 22E40; Secondary 53C24, 20G30, 11E08
DOI: https://doi.org/10.1090/tran/6970
Published electronically: August 15, 2017
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Abstract: In this paper we show that totally geodesic subspaces determine the commensurability class of a standard arithmetic hyperbolic $ n$-orbifold, $ n\ge 4$. Many of the results are more general and apply to locally symmetric spaces associated to arithmetic lattices in $ \mathbb{R}$-simple Lie groups of type $ B_n$ and $ D_n$. We use a combination of techniques from algebraic groups and quadratic forms to prove several results about these spaces.


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Additional Information

Jeffrey S. Meyer
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Address at time of publication: Department of Mathematics, California State University, San Bernardino, California 92407
Email: jeffrey.meyer@csusb.edu

DOI: https://doi.org/10.1090/tran/6970
Received by editor(s): June 9, 2015
Published electronically: August 15, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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