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Article Dans Une Revue Geometric And Functional Analysis Année : 2011

On the Second Cohomology of Kähler Groups

Résumé

Carlson and Toledo conjectured that if an infinite group Γ is the fundamental group of a compact Kähler manifold, then virtually H^2(Γ,ℝ)≠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 a ℂ -VHS.

Dates et versions

hal-01275541 , version 1 (17-02-2016)

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Bruno Klingler, Vincent Koziarz, Julien Maubon. On the Second Cohomology of Kähler Groups. Geometric And Functional Analysis, 2011, 21 (2), ⟨10.1007/s00039-011-0114-y⟩. ⟨hal-01275541⟩
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