## Abstract

We show the triviality of representations of the mapping class group of a genus g surface in GL(n, C), Diff (S) and Homeo(T) when appropriate restrictions on the genus g and the size of n hold. For example, if S is a surface of finite type with genus g > 3 and φ: MCG(S) → GL(n, C) is a homomorphism, then φ is trivial provided n < 2g. We also show that if S is a closed surface with genus g > 7, then every homomorphism φ: MCG(S) -y Diff(S ^{2}) is trivial and that if g > 3, then every homomorphism φ: MCG(S) → Homeo(T^{2}) is trivial.

Original language | English (US) |
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Pages (from-to) | 2951-2962 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 141 |

Issue number | 9 |

DOIs | |

State | Published - 2013 |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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