Arbitrarily large families of spaces of the same volume
Group Theory
2012-12-27 v2 Geometric Topology
Abstract
In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.
Keywords
Cite
@article{arxiv.1107.3043,
title = {Arbitrarily large families of spaces of the same volume},
author = {Vincent Emery},
journal= {arXiv preprint arXiv:1107.3043},
year = {2012}
}
Comments
9 pages. Syntax corrected; one reference added