On the second cohomology of Kähler groups

Carlson and Toledo conjectured that any infinite fundamental group $Γ$ of a compact Kähler manifold satisfies $H^2(Γ,\R)\not =0$. We assume that $Γ$ admits an unbounded reductive rigid linear representation. This representation necessarily comes from a complex variation of Hodge structure ($\C$-VHS) on the Kähler manifold. We prove the conjecture under some assumption on the $\C$-VHS. We also study some related geometric/topological properties of period domains associated to such $\C$-VHS.

No reviews yet.

No comments yet.