On fibered commensurability
Geometric Topology
2011-04-04 v2 Dynamical Systems
Abstract
This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over the circle. We show that every hyperbolic fibered commensurability class contains a unique minimal element, whereas the class of Seifert manifolds fibering over the circle consists of a single commensurability class with infinitely many minimal elements. The situation for non-geometric manifolds is more complicated, and we illustrate a range of phenomena that can occur in this context.
Keywords
Cite
@article{arxiv.1003.0411,
title = {On fibered commensurability},
author = {Danny Calegari and Hongbin Sun and Shicheng Wang},
journal= {arXiv preprint arXiv:1003.0411},
year = {2011}
}
Comments
26 pages, 16 figures; version 2 incorporates referee's comments