Exponential growth of homological torsion for towers of congruence subgroups of Bianchi groups

2013/02/13 by Jonathan Pfaff, Pfaff, Jonathan
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.DG #math.GT #math.NT

paper · pdf · doi:10.48550/arxiv.1302.3079

arxiv created 2013/02/13 · openalex publication_date 2013/02/13 · arxiv updated 2013/02/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that for suitable sequences of congruence subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of Sl₂(C) the size of the torsion part in the first homology grows exponentially. This extends results of Bergeron and Venkatesh to a case of non-uniform lattices.

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