On the torsion in symmetric powers on congruence subgroups of Bianchi groups
Abstract
In this paper we prove that for a fixed neat principal congruence subgroup of a Bianchi group the order of the torsion part of its second cohomology group with coefficients in an integral lattice associated to the m-th symmetric power of the standard representation of SL_2(C) grows exponentially in m^2. We give upper and lower bounds for the growth rate. Our result extends a result of Mueller and Marshall, who proved the corresponding statement for closed arithmetic 3-manifolds, to the finite-volume case. We also prove a limit multiplicity formula for twisted combinatorial Reidemeister torsion on higher dimensional hyperbolic manifolds.
Keywords
Cite
@article{arxiv.1503.04785,
title = {On the torsion in symmetric powers on congruence subgroups of Bianchi groups},
author = {Jonathan Pfaff and Jean Raimbault},
journal= {arXiv preprint arXiv:1503.04785},
year = {2015}
}
Comments
Second version : 35 pages, we made minor corrections and added a cheap but substantial improvement of the main result