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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 |
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Algebraic & Geometric Topology 9 (2009) 1177–1199
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Abstract |
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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 moduli space vanishes. In the genus one case, this cohomology group is infinite dimensional. |
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Keywords
group cohomology, mapping class group, flat connection,
moduli space
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Mathematical Subject Classification 2000
Primary: 20J06
Secondary: 57M07, 57M60
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References |
Publication
Received: 24 October 2008
Revised: 13 May 2009
Accepted: 13 May 2009
Published: 10 June 2009
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Authors |
| Jørgen Ellegaard Andersen | |
| Department of Mathematics University of Aarhus 8000 Aarhus C Denmark |
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| http://home.imf.au.dk/andersen/ | |
| Rasmus Villemoes | |
| Department of Mathematics University of Aarhus 8000 Aarhus C Denmark |
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| http://www.rasmusvillemoes.dk | |
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