On the second cohomology of Kähler groups

Details On the second cohomology of Kähler groups On the second cohomology of Kähler groups

2010-04-19

arxiv.org/abs/1004.3130v2

Mathematics

Differential Geometry

21 pages. Exposition improved. Final version

Scientific paper

Carlson and Toledo conjectured that any infinite fundamental group $\Gamma$ of a compact K\"ahler manifold satisfies $H^2(\Gamma,\R)\not =0$. We assume that $\Gamma$ admits an unbounded reductive rigid linear representation. This representation necessarily comes from a complex variation of Hodge structure ($\C$-VHS) on the K\"ahler 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.

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