## 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

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

#### Article information

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

Dates
Revised: 13 May 2009
Accepted: 13 May 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513797011

Digital Object Identifier
doi:10.2140/agt.2009.9.1177

Mathematical Reviews number (MathSciNet)
MR2511142

Zentralblatt MATH identifier
1243.20065

#### Citation

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. https://projecteuclid.org/euclid.agt/1513797011

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