Triviality of some representations of MCG(Sg) in GL(n, C), Diff S2) and Homeo(T2)

John M Franks, Michael Handel

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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(T2) is trivial.

Original languageEnglish (US)
Pages (from-to)2951-2962
Number of pages12
JournalProceedings of the American Mathematical Society
Volume141
Issue number9
DOIs
StatePublished - Jun 28 2013

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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