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arXiv · 1408.2579

Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces

Jeffrey S. Meyer
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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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BibTeXRIS

Jeffrey S. Meyer. 2014-08-11. Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces. https://arxiv.org/abs/1408.2579

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