Displaying similar documents to “Weakly commensurable arithmetic groups and isospectral locally symmetric spaces”

On arithmetic Fuchsian groups and their characterizations

Slavyana Geninska (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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This is a small survey paper about connections between the arithmetic and geometric properties in the case of arithmetic Fuchsian groups.

Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups

Filling Bestvina, Alex Eskin, Kevin Wortman (2013)

Journal of the European Mathematical Society

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We provide partial results towards a conjectural generalization of a theorem of Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields or function fields) that implies, in low dimensions, both polynomial isoperimetric inequalities and finiteness properties. As a tool in our proof, we establish polynomial isoperimetric inequalities and finiteness properties for certain solvable groups that appear as subgroups of parabolic groups in semisimple groups, thus generalizing a...

On volumes of arithmetic quotients of S O ( 1 , n )

Mikhail Belolipetsky (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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 S O ( 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-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic...

Addendum to: On volumes of arithmetic quotients of SO (1, n)

Mikhail Belolipetsky (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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There are errors in the proof of uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.