Analytic, Reidemeister and homological torsion for congruence three--manifolds
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2013
- DOI:
- 10.48550/arXiv.1307.2845
- arXiv:
- arXiv:1307.2845
- Bibcode:
- 2013arXiv1307.2845R
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Number Theory;
- 11F75;
- 22E40;
- 57M10
- E-Print:
- 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