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

Permanent link to this document
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

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

Keywords
group cohomology mapping class group flat connection moduli space

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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