Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces

2014/08/11 by Meyer, Jeffrey S.
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1408.2579

Abstract

In this paper we show that totally geodesic subspaces determine the commensurability class of a standard arithmetic hyperbolic n-orbifold, n≥ 4. Many of the results are more general and apply to locally symmetric spaces associated to arithmetic lattices in 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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