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The first cohomology of the mapping class group with coefficients in algebraic functions on the SL(2, C) moduli space

arXiv:0802.4372 · doi:10.2140/agt.2009.9.1177

Abstract

Consider a compact surface of genus at least two. We prove that the first cohomology group of the mapping class group with coefficients in the space of algebraic functions on the SL(2, C) moduli space vanishes.