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On Volumes of Arithmetic Quotients of SO(1,n)

M. Belolipetsky
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Abstract

We apply G. Prasad's volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of SO(1,n). As a result we prove that for any even dimension n there exists a unique compact arithmetic hyperbolic n-orbifold of the smallest volume. We give a formula for the Euler-Poincare characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We also study hyperbolic 4-manifolds defined arithmetically and obtain a number theoretical characterization of the smallest compact arithmetic 4-manifold.

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BibTeXRIS

M. Belolipetsky. 2004-11-21. On Volumes of Arithmetic Quotients of SO(1,n). https://arxiv.org/abs/math/0306423

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