Cohomology of mapping class groups and the abelian moduli space
Cohomology of mapping class groups and the abelian moduli space
We consider a surface \Sigma of genus g \geq 3 , either closed or with exactly one puncture. The mapping class group \Gamma of \Sigma acts symplectically on the abelian moduli space M = \operatorname{Hom}(\pi_1(\Sigma), \operatorname{U}(1)) = \operatorname{Hom}(H_1(\Sigma), \operatorname{U}(1)) , and hence both L^2(M) and C^\infty(M) are modules over \Gamma …