On fibered commensurability

Abstract

This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over S1. We show that every hyperbolic fibered commensurability class contains a unique minimal element. The situation for toroidal manifolds is more complicated, and we illustrate a range of phenomena that can occur in this context. © 2011 Pacific Journal of Mathematics.