The asymptotic growth of torsion homology for arithmetic groups

2010/04/07 by Bergeron, Nicolas, Venkatesh, Akshay · 7 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1004.1083

Abstract

When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is so, and conjecture precise conditions.

Cited by

• Family of hyperbolic manifolds with exponential homology torsion growth
• L²-torsion of automorphisms
• On the integral simplicial volume of cyclic covers of mapping tori
• Virtual homological torsion: abundance versus growth in books of I-bundles
• Homological torsion growth in non-normal chains of graphs of free groups
• Asymptotics of analytic torsion for congruence quotients of SL(n,ℝ)/SO(n)
• The homology torsion growth of determinantal hypertrees

Related

• On homology torsion growth
• On the growth of torsion in the cohomology of arithmetic groups
• Family of hyperbolic manifolds with exponential homology torsion growth
• The cheap embedding principle: Dynamical upper bounds for homology growth
• On the growth of torsion in the cohomology of arithmetic groups