On commensurability of fibrations on a hyperbolic 3-manifold

Hidetoshi Masai

Vol. 266 (2013), No. 2, 313–327

DOI: 10.2140/pjm.2013.266.313

Abstract

We discuss fibered commensurability of fibrations on hyperbolic 3-manifolds, a notion introduced by Calegari, Sun, and Wang (Pacific J. Math. 250:2 (2011), 287–317). We construct manifolds with nonsymmetric but commensurable fibrations on the same fibered face, and prove that if a given manifold M does not have hidden symmetries, then M does not admit nonsymmetric but commensurable fibrations.

It was also proved by Calegari et al that every hyperbolic fibered commensurability class contains a unique minimal element. Here we provide a detailed discussion on the proof of the theorem in the cusped case.

Keywords

hyperbolic manifold, fibration, commensurability

Mathematical Subject Classification 2010

Primary: 57M50

Secondary: 37B40

Milestones

Received: 24 October 2012

Revised: 2 July 2013

Accepted: 5 July 2013

Published: 12 November 2013