Totally geodesic spectra of arithmetic hyperbolic spaces
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- by Jeffrey S. Meyer PDF
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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.References
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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
- MR Author ID: 1064837
- Email: jeffrey.meyer@csusb.edu
- Received by editor(s): June 9, 2015
- Published electronically: August 15, 2017
- © Copyright 2017 American Mathematical Society
- 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
- MathSciNet review: 3695838