Degree one cohomology with twisted coefficients of the mapping class group

Abstract

Let $\Gamma$ be the mapping class group of an oriented surface $\Sigma$ of genus g with r boundary components. We prove that the first cohomology group $H^1(\Gamma ,O(M_{SL(2,C)}{)}^{\ast })$ is non-trivial, where the coefficient module is the dual of the space of algebraic functions on the $SL(2,C)$ moduli space over $\Sigma$.

arXiv comment19 pages, 11 figures

References in corpus (1)

• Hitchin's connection, Toeplitz operators and symmetry invariant deformation quantization

Cited by in corpus (4)

• Hitchin's Projectively Flat Connection, Toeplitz Operators and the Asymptotic Expansion of TQFT Curve Operators
• Asymptotics of Toeplitz operators and applications in TQFT
• The mapping class group orbit of a multicurve
• Cohomology of mapping class groups and the abelian moduli space