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Normalized entropy versus
volume for pseudo-Anosovs
Sadayoshi Kojima and Greg McShane |
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Geometry & Topology 22 (2018) 2403–2426
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Abstract |
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Thanks to a recent result by Jean-Marc Schlenker, we establish an explicit linear inequality between the normalized entropies of pseudo-Anosov automorphisms and the hyperbolic volumes of their mapping tori. As corollaries, we give an improved lower bound for values of entropies of pseudo-Anosovs on a surface with fixed topology, and a proof of a slightly weaker version of the result by Farb, Leininger and Margalit first, and by Agol later, on finiteness of cusped manifolds generating surface automorphisms with small normalized entropies. Also, we present an analogous linear inequality between the Weil–Petersson translation distance of a pseudo-Anosov map (normalized by multiplying by the square root of the area of a surface) and the volume of its mapping torus, which leads to a better bound. |
Keywords
mapping class, entropy, mapping torus, Weil-Petersson
metric , Teichmüller translation distance, hyperbolic
volume
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 37E30
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References |
Publication
Received: 9 December 2016
Revised: 16 May 2017
Accepted: 23 June 2017
Published: 5 April 2018
Proposed: Benson Farb
Seconded: Dmitri Burago, Ian Agol
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Authors |
| Sadayoshi Kojima | |
| Department of Mathematical and
Computing Sciences Tokyo Institute of Technology Tokyo Japan |
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| Greg McShane | |
| UFR de Mathématiques Institut Fourier St Martin d’Hères France |
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