Vol. 266, No. 2, 2013

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On commensurability of fibrations on a hyperbolic 3-manifold

Hidetoshi Masai

Vol. 266 (2013), No. 2, 313–327
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
Authors
Hidetoshi Masai
Department of Mathematical and Computing Sciences
Tokyo Institute of Technology
2-12-1 O-okayama, Meguro-ku
Tokyo 152-8552
Japan