2012/10/31 by Hidetoshi Masai
Mathematics · #3-manifold #Commensurability (mathematics) #Fibered knot #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Homogeneous space #Hyperbolic 3-manifold #Hyperbolic function #Hyperbolic manifold #Manifold (fluid mechanics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Pure mathematics #Relatively hyperbolic group #math.DS #math.GT #msc:37B40 #msc:57M50
paper · pdf · doi:10.2140/pjm.2013.266.313
published as Pacific J. Math. 266 (2013) 313-327 · 12 pages, 3 figures, version 3 is reorganized following referee's suggestions, version 2 has problems on showing figures
arxiv created 2013/07/09 · openalex publication_date 2013/11/12 · arxiv updated 2016/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.