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2009 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, Rasmus Villemoes
Algebr. Geom. Topol. 9(2): 1177-1199 (2009). 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 SL2(C) moduli space vanishes. In the genus one case, this cohomology group is infinite dimensional.

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Jørgen Ellegaard Andersen. Rasmus Villemoes. "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 (2) 1177 - 1199, 2009. https://doi.org/10.2140/agt.2009.9.1177

Information

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

zbMATH: 1243.20065
MathSciNet: MR2511142
Digital Object Identifier: 10.2140/agt.2009.9.1177

Subjects:
Primary: 20J06
Secondary: 57M07, 57M60

Rights: Copyright © 2009 Mathematical Sciences Publishers

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