On the second cohomology of K\"ahler groups

Bruno Klingler; Vincent Koziarz; Julien Maubon

On the second cohomology of K\"ahler groups

Differential Geometry 2010-12-10 v2 Algebraic Geometry Geometric Topology

Authors: Bruno Klingler , Vincent Koziarz , Julien Maubon

Abstract

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.

Keywords

Kähler group second cohomology fundamental group complex variation of Hodge structure reductive rigid representation period domain

Cite

@article{arxiv.1004.3130,
  title  = {On the second cohomology of K\"ahler groups},
  author = {Bruno Klingler and Vincent Koziarz and Julien Maubon},
  journal= {arXiv preprint arXiv:1004.3130},
  year   = {2010}
}

Comments

21 pages. Exposition improved. Final version

On the second cohomology of K\"ahler groups

Abstract

Keywords

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