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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Totally geodesic spectra of arithmetic hyperbolic spaces
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by Jeffrey S. Meyer PDF
Trans. Amer. Math. Soc. 369 (2017), 7549-7588 Request permission

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
  • 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