### Abstract

The aim of this note is to give the simplest possible proof that Mapping Class Groups of closed hyperbolic surfaces are acylindrically hyperbolic, and more specifically that their curve graphs are hyperbolic and that pseudo-Anosovs act on them as loxodromic WPDs.

Original language | English |
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Title of host publication | Hyperbolic Geometry and Geometric Group Theory |

Editors | Koji Fujiwara, Sadayoshi Kojima, Ken'ichi Ohshika |

Publisher | Mathematical Society of Japan |

Pages | 255-264 |

Number of pages | 10 |

ISBN (Print) | 978-4-86497-043-3, 978-4-86497-042-6 |

DOIs | |

Publication status | Published - 2017 |

### Publication series

Name | Advanced Studies in Pure Mathematics |
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Publisher | Mathematical Society of Japan |

Volume | 73 |

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## Cite this

Przytycki, P., & Sisto, A. (2017). A note on acylindrical hyperbolicity of mapping class groups. In K. Fujiwara, S. Kojima, & K. Ohshika (Eds.),

*Hyperbolic Geometry and Geometric Group Theory*(pp. 255-264). (Advanced Studies in Pure Mathematics; Vol. 73). Mathematical Society of Japan. https://doi.org/10.2969/aspm/07310255