### 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 |

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### Keywords

- Euler number
- Surface group action
- Topological entropy

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics