Volume 9, issue 2 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
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.

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