Cohomological rigidity of irreducible Mod_{g,n}-representations

Establish that for genus g≥3, every irreducible complex representation \rho of the mapping class group Mod_{g,n} is cohomologically rigid, i.e., H^1(Mod_{g,n},\operatorname{ad}(\rho))=0.

Background

Motivated by superrigidity phenomena for lattices in higher-rank Lie groups, this conjecture strengthens Ivanov’s finite abelianization conjecture by positing that all irreducible representations of Mod_{g,n} admit no nontrivial first-order deformations.