On the cohomology of Kaehler groups

2010/05/17 by Bruno Klingler, Klingler, Bruno
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.AT #math.DG #math.GR

paper · pdf · doi:10.48550/arxiv.1005.2835

arxiv created 2010/05/17 · arxiv updated 2010/05/18

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).

Related

• Kaehler groups and duality
• Homomorphisms between Kaehler groups
• Structure of Kahler groups, I: second cohomology
• Cohomology of Kaehler manifolds with c₁=0
• Harmonic bundles on quasi-compact Kaehler manifolds