On commensurability of fibrations on a hyperbolic 3-manifold

Abstract

We discuss fibered commensurability of fibrations on a hyperbolic 3-manifold, a notion introduced by Calegari, Sun and Wang. We construct manifolds with non-symmetric but commensurable fibrations on the same fibered face. We also prove that if a given manifold M does not have any hidden symmetries, then M does not admit non-symmetric but commensu- rable fibrations. Finally, Theorem 3.1 of Calegari, Sun and Wang shows that every hyperbolic fibered commensurability class contains a unique minimal element. In this paper we provide a detailed discussion on the proof of the theorem in the cusped case.

12 pages, 3 figures, version 3 is reorganized following referee's suggestions, version 2 has problems on showing figures

References in corpus (2)

• Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behavior
• Commensurability of two-multitwist pseudo-Anosovs

Cited by in corpus (4)

• Fibered commensurability and arithmeticity of random mapping tori
• On commensurability of quadratic differentials
• Fibered commensurability on $\mathrm{Out}(F_n)$
• On the number of commensurable fibrations on a hyperbolic 3-manifold