### 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 language | English |
---|---|

Pages (from-to) | 3993-4002 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2012 Jul 23 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Entropy, weil-petersson translation distance and gromov norm for surface automorphisms.** / Kojima, Sadayoshi.

Research output: Contribution to journal › Article

}

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

UR - http://www.scopus.com/inward/record.url?scp=84863956287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863956287&partnerID=8YFLogxK

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

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

M3 - Article

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 -