TY - JOUR

T1 - Entropy, weil-petersson translation distance and gromov norm for surface automorphisms

AU - Kojima, Sadayoshi

PY - 2012/7/23

Y1 - 2012/7/23

N2 - 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.

AB - 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.

KW - Entropy

KW - Gromov norm

KW - Surface automorphism

KW - Teichm̈uller translation distance

KW - Weil-petersson translation distance

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U2 - 10.1090/S0002-9939-2012-11250-X

DO - 10.1090/S0002-9939-2012-11250-X

M3 - Article

AN - SCOPUS:84863956287

VL - 140

SP - 3993

EP - 4002

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -