Ivanov’s finite abelianization conjecture for Mod_{g,n}

Show that for genus g≥3, every finite-index subgroup Γ of the mapping class group Mod_{g,n} has finite abelianization, i.e., H^1(Γ,\mathbb{C})=0.

Background

This classical conjecture reflects analogies between mapping class groups and higher-rank lattices, predicting ‘superrigidity-type’ behavior for Mod_{g,n}. The paper relates it to stronger cohomological rigidity expectations for representations of Mod_{g,n}.