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On volumes of arithmetic quotients of SO(1, n)

Belolipetsky, M.

Authors

M. Belolipetsky



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.

Citation

Belolipetsky, M. (2004). On volumes of arithmetic quotients of SO(1, n). Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 3(4), 749-770

Journal Article Type Article
Publication Date 2004-11
Deposit Date May 1, 2007
Journal Annali della Scuola normale superiore di Pisa, Classe di scienze.
Print ISSN 0391-173X
Publisher Scuola Normale Superiore - Edizioni della Normale
Peer Reviewed Peer Reviewed
Volume 3
Issue 4
Pages 749-770
Keywords Subgroups.
Publisher URL http://www.sns.it/en/edizioni/riviste/annaliscienze/

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