Arbitrarily large families of spaces of the same volume
arXiv:1107.3043 · doi:10.1007/s10711-011-9684-y
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.
9 pages. Syntax corrected; one reference added