Entropy, weil-petersson translation distance and gromov norm for surface automorphisms

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Abstract

Thanks to a theorem of Brock on the comparison ofWeil-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 a Gromov norm of its mapping torus from below and an inbounded 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.

Original languageEnglish
Pages (from-to)3993-4002
Number of pages10
JournalProceedings of the American Mathematical Society
Volume140
Issue number11
DOIs
Publication statusPublished - 2012 Jul 23

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Keywords

  • Entropy
  • Gromov norm
  • Surface automorphism
  • Teichm̈uller translation distance
  • Weil-petersson translation distance

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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