Entropy, Weil-Petersson translation distance and Gromov norm for surface automorphisms

2010/04/13 by Sadayoshi Kojima, Kojima, Sadayoshi · 1 citation
Mathematics · #57M50 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Primary 37E30 #Secondary 57M27

paper · pdf · doi:10.48550/arxiv.1004.2109

openalex publication_date 2010/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Thanks to a theorem of Brock on comparison of Weil-Petersson translation distances and hyperbolic volumes of mapping tori for pseudo-Anosovs, we prove that the entropy of a surface automorphism in general has linear bounds in terms of Gromov norm of its mapping torus from below and in bounded geometry case from above. We also prove that the Weil-Petersson translation distance does the same from both sides in general. The proofs are in fact immediately derived from the theorem of Brock together with some other strong theorems and small observations.

Citations

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
• Asymptotics of Weil-Petersson geodesics II: bounded geometry and unbounded entropy

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• Ribbon concordance and fibered predecessors

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