Exponential growth of homological torsion for towers of congruence subgroups of Bianchi groups |
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Authors: | Jonathan Pfaff |
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Institution: | 1. Mathematisches Institut, Universit?t Bonn, Endenicher Alle 60, 53115?, Bonn, Germany
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Abstract: | In this paper we prove that for suitable sequences of subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of $\mathrm{SL }_2(\mathbb {C})$ the size of the torsion part in the first integral homology grows exponentially. This extends results of Bergeron and Venkatesh to a case of non-uniform lattices. Our approach is geometric. For odd symmetric powers we obtain a modified statement. |
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