Algebraic & Geometric Topology

The first cohomology of the mapping class group with coefficients in algebraic functions on the $\mathrm{SL}_2(\mathbf{C})$ moduli space

Jørgen Ellegaard Andersen and Rasmus Villemoes

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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 SL2(C) moduli space vanishes. In the genus one case, this cohomology group is infinite dimensional.

Article information

Algebr. Geom. Topol., Volume 9, Number 2 (2009), 1177-1199.

Received: 24 October 2008
Revised: 13 May 2009
Accepted: 13 May 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20J06: Cohomology of groups
Secondary: 57M07: Topological methods in group theory 57M60: Group actions in low dimensions

group cohomology mapping class group flat connection moduli space


Andersen, Jørgen Ellegaard; Villemoes, Rasmus. The first cohomology of the mapping class group with coefficients in algebraic functions on the $\mathrm{SL}_2(\mathbf{C})$ moduli space. Algebr. Geom. Topol. 9 (2009), no. 2, 1177--1199. doi:10.2140/agt.2009.9.1177.

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