Analytic, Reidemeister and homological torsion for congruence three--manifolds

2013/07/10 by Jean Raimbault, Raimbault, Jean
Mathematics · #11F75 #22E40 #57M10 #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT) #math.GT #math.NT #msc:11F75 #msc:22E40 #msc:57M10

paper · pdf · doi:10.48550/arxiv.1307.2845

Overdue update, the main result has been much weakened due to a gap in the last step of the proof (we get only an upper bound on the limsup instead of a limit). We include a conditional statement of the previous version, however checking the condition seems hard

arxiv created 2018/02/13 · arxiv updated 2018/02/14

Abstract

Starting from the results in math.DG:1212.3161 we prove that for a given Bianchi group, certain natural coefficent modules and a lot of sequences of congruence subgroups of the size of the torsion subgroup of the first homology grows exponentially with the index (we give an explicit rate). We also prove limit multiplicity results for the irreducible components of the space of cuspidal forms.

Related

• On the torsion in symmetric powers on congruence subgroups of Bianchi groups
• Exponential growth of homological torsion for towers of congruence subgroups of Bianchi groups
• On the growth of torsion in the cohomology of some arithmetic groups of ℚ-rank one
• Analytic torsion and Reidemeister torsion of hyperbolic manifolds with cusps
• The asymptotic growth of torsion homology for arithmetic groups