We consider a surface of genus , either closed or with exactly one puncture. The mapping class group of acts symplectically on the abelian moduli space , and hence both and are modules over . In this paper, we prove that both the cohomology groups and vanish.
Cite this article
Jørgen Ellegaard Andersen, Rasmus Villemoes, Cohomology of mapping class groups and the abelian moduli space. Quantum Topol. 3 (2012), no. 3/4, pp. 359–376DOI 10.4171/QT/32