TY - JOUR

T1 - Triviality of some representations of MCG(Sg) in GL(n, C), Diff S2) and Homeo(T2)

AU - Franks, John M

AU - Handel, Michael

PY - 2013/6/28

Y1 - 2013/6/28

N2 - 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.

AB - 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.

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U2 - 10.1090/S0002-9939-2013-11556-X

DO - 10.1090/S0002-9939-2013-11556-X

M3 - Article

AN - SCOPUS:84879312310

VL - 141

SP - 2951

EP - 2962

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -