### Abstract

In this paper, we show that a surface group action on s^{1} with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.

Original language | English |
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Pages (from-to) | 245-249 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 106 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1989 |

### Fingerprint

### Keywords

- Euler number
- Surface group action
- Topological entropy

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**On topological entropy of group actions on s.** / Watanabe, Nobuya.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 106, no. 1, pp. 245-249. https://doi.org/10.1090/S0002-9939-1989-0965946-X

}

TY - JOUR

T1 - On topological entropy of group actions on s

AU - Watanabe, Nobuya

PY - 1989

Y1 - 1989

N2 - In this paper, we show that a surface group action on s1 with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.

AB - In this paper, we show that a surface group action on s1 with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.

KW - Euler number

KW - Surface group action

KW - Topological entropy

UR - http://www.scopus.com/inward/record.url?scp=84966231342&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966231342&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1989-0965946-X

DO - 10.1090/S0002-9939-1989-0965946-X

M3 - Article

VL - 106

SP - 245

EP - 249

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -