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

Belolipetsky, M.

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
• Electronic ISSN: 2036-2145
• Publisher: Scuola Normale Superiore - Edizioni della Normale
• Peer Reviewed: Peer Reviewed
• Volume: 3
• Issue: 4
• Pages: 749-770
• Keywords: Subgroups.
• Public URL: https://durham-repository.worktribe.com/output/1585612
• Publisher URL: http://www.sns.it/en/edizioni/riviste/annaliscienze/