1. On the second cohomology of K��hler groups
- Author
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Klingler, Bruno, Koziarz, Vincent, and Maubon, Julien
- Subjects
Differential Geometry (math.DG) ,Condensed Matter::Superconductivity ,FOS: Mathematics ,Geometric Topology (math.GT) ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,Algebraic Geometry (math.AG) - Abstract
Carlson and Toledo conjectured that any infinite fundamental group $��$ of a compact K��hler manifold satisfies $H^2(��,\R)\not =0$. We assume that $��$ admits an unbounded reductive rigid linear representation. This representation necessarily comes from a complex variation of Hodge structure ($\C$-VHS) on the K��hler 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., 21 pages. Exposition improved. Final version
- Published
- 2010
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