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Journal Article

# TWO QUESTIONS ON MAPPING CLASS GROUPS

LOUIS FUNAR
Proceedings of the American Mathematical Society
Vol. 139, No. 1 (JANUARY 2011), pp. 375-382
Stable URL: http://www.jstor.org/stable/41059224
Page Count: 8

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Topics: Homomorphisms, Polynomials, Algebra, Fixed point property, Integers, Eigenvalues, Signatures, Fractions

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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 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 $SL([\sqrt {g + 1} ],{\Bbb C})$ ) have finite image. Both results come from properties of quantum representations of mapping class groups.

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