Counting non-commensurable hyperbolic manifolds and a bound on homological torsion
Geometric Topology
2017-09-07 v1
Abstract
We prove that the cardinality of the torsion subgroups in homology of a closed hyperbolic manifold of any dimension can be bounded by a doubly exponential function of its diameter. It would follow from a conjecture by Bergeron and Venkatesh that the order of growth in our bound is sharp. We also determine how the number of non-commensurable closed hyperbolic manifolds of dimension at least 3 and bounded diameter grows. The lower bound implies that the fraction of arithmetic manifolds tends to zero as the diameter goes up.
Keywords
Cite
@article{arxiv.1709.01873,
title = {Counting non-commensurable hyperbolic manifolds and a bound on homological torsion},
author = {Bram Petri},
journal= {arXiv preprint arXiv:1709.01873},
year = {2017}
}
Comments
15 pages, 1 figure