Vol. 250, No. 2, 2011

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On fibered commensurability

Danny Calegari, Hongbin Sun and Shicheng Wang

Vol. 250 (2011), No. 2, 287–317
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.

Keywords
commensurability, fibration, 3-manifold, mapping class group
Mathematical Subject Classification 2000
Primary: 57M50
Milestones
Received: 7 April 2010
Accepted: 21 June 2010
Published: 31 March 2011
Authors
Danny Calegari
Department of Mathematics
California Insitute of Technology
Pasadena CA 91125
United States
http://www.its.caltech.edu/~dannyc
Hongbin Sun
Department of Mathematics
Princeton University
Fine Hall, Room 304
Washington Road
Princeton NJ 08544
United States
Shicheng Wang
School of Mathematical Sciences
Peking University
Beijing, 100871
China