Arithmetic Kleinian groups generated by elements of finite order
Geometric Topology
2017-07-11 v2 Group Theory
Metric Geometry
Abstract
We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. This implies, in particular, that there exist only finitely many conjugacy classes of cocompact two generated arithmetic Kleinian groups. The proof of the main result is based on a generalized Gromov--Guth inequality and bounds for the hyperbolic and tube volumes of the quotient orbifolds.
Cite
@article{arxiv.1610.06147,
title = {Arithmetic Kleinian groups generated by elements of finite order},
author = {Mikhail Belolipetsky},
journal= {arXiv preprint arXiv:1610.06147},
year = {2017}
}
Comments
18 pages; v2: filled a critical gap in Theorem 2.2, section 6 is preliminary and will be updated later