2010/04/19 by Bruno Klingler, Klingler, Bruno, Vincent Koziarz +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #math.AG #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.1004.3130
21 pages. Exposition improved. Final version
openalex publication_date 2010/04/19 · arxiv created 2010/12/09 · arxiv updated 2010/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Carlson and Toledo conjectured that any infinite fundamental group Γ of a compact Kähler manifold satisfies H2(Γ,\R)\not =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 \C-VHS.