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arXiv · 1005.2835

On the cohomology of Kaehler groups

Bruno Klingler
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Abstract

This is the geometric part of two papers on the cohomology of Kaehler groups. Using non-Abelian Hodge theory we show that if a finitely presented group with an unbounded complex linear morphism is the fundamental group of a compact Kaehler manifold then its second or its fourth Betti number does not vanish. Combined with our first paper this shows that a cocompact lattice in a real simple Lie group G of sufficiently large real rank is Kaehler if and only if G is of Hermitian type (a conjecture of Carlson and Toledo).

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BibTeXRIS

Bruno Klingler. 2010-05-17. On the cohomology of Kaehler groups. https://arxiv.org/abs/1005.2835

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