Two questions on mapping class groups

Funar, Louis

doi:10.1090/S0002-9939-2010-10555-5

Two questions on mapping class groups
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by Louis Funar

Proc. Amer. Math. Soc. 139 (2011), 375-382

DOI: https://doi.org/10.1090/S0002-9939-2010-10555-5

Published electronically: August 5, 2010

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Abstract:

We show that central extensions of the mapping class group $M_g$ of the closed orientable surface of genus $g$ by $\mathbb {Z}$ are residually finite. Further we give rough estimates of the largest $N=N_g$ such that homomorphisms from $M_g$ to $SU(N)$ have finite image. In particular, homomorphisms of $M_g$ into $SL([\sqrt {g+1}],\mathbb {C})$ have finite image. Both results come from properties of quantum representations of mapping class groups.

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