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

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.

commensurability, fibration, 3-manifold, mapping class group
Mathematical Subject Classification 2000
Primary: 57M50
Received: 7 April 2010
Accepted: 21 June 2010
Published: 31 March 2011
Danny Calegari
Department of Mathematics
California Insitute of Technology
Pasadena CA 91125
United States
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