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We show the triviality of representations of the mapping class group of agenus $g$ surface in $GL(n,C), Diff(S^2)$ and $Homeo(T^2)$ when appropriaterestrictions on the genus $g$ and the size of $n$ hold. For example, if $S_g$is a surface of finite type and $\phi : MCG(S_g) \to GL(n,C)$ is ahomomorphism, then $\phi$ is trivial provided the genus $g \ge 3$ and $n < 2g$.We also show that if $S_g$ is a closed surface with genus $g \ge 7$, then everyhomomorphism $\phi: MCG(S_g) \to Diff(S^2)$ is trivial and that if $g \ge 3$,then every homomorphism $\phi: MCG(S_g) \to Homeo(T^2)$ is trivial.

Triviality of some representations of $MCG(S_g)$ in $GL(n,C), Diff(S^2)$ and $Homeo(T^2)$