The first cohomology of the mapping class group with coefficients in algebraic functions on the SL2(C) moduli space

Andersen, Jørgen Ellegaard; Villemoes, Rasmus

doi:10.2140/agt.2009.9.1177

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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

Algebraic & Geometric Topology 9 (2009) 1177–1199

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. In the genus one case, this cohomology group is infinite dimensional.

Keywords

group cohomology, mapping class group, flat connection, moduli space

Mathematical Subject Classification 2000

Primary: 20J06

Secondary: 57M07, 57M60

References

Publication

Received: 24 October 2008

Revised: 13 May 2009

Accepted: 13 May 2009

Published: 10 June 2009

Authors

Jørgen Ellegaard Andersen
Department of Mathematics University of Aarhus 8000 Aarhus C Denmark
http://home.imf.au.dk/andersen/
Rasmus Villemoes
Department of Mathematics University of Aarhus 8000 Aarhus C Denmark
http://www.rasmusvillemoes.dk

Volume 9, issue 2 (2009)