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

Author: Sadayoshi Kojima
Journal: Proc. Amer. Math. Soc. 140 (2012), 3993-4002
MSC (2010): Primary 37E30; Secondary 57M27, 57M50
Published electronically: March 28, 2012
MathSciNet review: 2944738
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Abstract: Thanks to a theorem of Brock on the 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 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.

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Additional Information

Sadayoshi Kojima
Affiliation: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo 152-8552, Japan

Keywords: Surface automorphism, entropy, Teichmüller translation distance, Weil-Petersson translation distance, Gromov norm.
Received by editor(s): May 6, 2010
Received by editor(s) in revised form: March 6, 2011, and May 13, 2011
Published electronically: March 28, 2012
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (A) (No. 22244004), JSPS, Japan
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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