Entropy, Weil-Petersson translation distance and Gromov norm for surface automorphisms
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- by Sadayoshi Kojima
- Proc. Amer. Math. Soc. 140 (2012), 3993-4002
- DOI: https://doi.org/10.1090/S0002-9939-2012-11250-X
- Published electronically: March 28, 2012
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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.References
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Bibliographic Information
- Sadayoshi Kojima
- Affiliation: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro, Tokyo 152-8552, Japan
- Email: sadayosi@is.titech.ac.jp
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3993-4002
- MSC (2010): Primary 37E30; Secondary 57M27, 57M50
- DOI: https://doi.org/10.1090/S0002-9939-2012-11250-X
- MathSciNet review: 2944738