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arXiv · 1004.3130

On the second cohomology of Kähler groups

Bruno Klingler·Vincent Koziarz·Julien Maubon
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Abstract

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.

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Bruno Klingler, Vincent Koziarz, Julien Maubon. 2010-12-09. On the second cohomology of Kähler groups. https://arxiv.org/abs/1004.3130

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