The fundamental group of Kaehler manifolds

It studies the fundamental group of complex algebraic varieties, in its Betti, Hodge and de Rham realizations. This study has been carried out both in the absolute case, i.e. fundamental groups of such varieties, and in the relative case, where one studies the monodromy in the fundamental group and the associated Gauss-Manin connection. The three main lines of research have been: (i) The unipotent completion of Kaehler groups, by means of Sullivan's 1-minimal models and formality. (ii) The monodromy in the fundmental group in families of curves with ordinary quadratic singularities. (iii) The 1-minimal model of the Gauss-Manin connection in the cohomology of families of algebraic manifolds.

Country

Spain

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Keywords

Teoria d', :14 Algebraic geometry::14F (Co)homology theory [Classificació AMS], Classificació AMS::53 Differential geometry::53C Global differential geometry, Geometria diferencial, Homologia, Classificació AMS::14 Algebraic geometry::14F (Co)homology theory, Espais analítics, Classificació AMS::32 Several complex variables and analytic spaces::32J Compact analytic spaces, monodromy in the fundamental group, Homologia, Teoria d', :53 Differential geometry::53C Global differential geometry [Classificació AMS], Kaehler group, Homology theory, Malcev algebra, irrational pencil, :32 Several complex variables and analytic spaces::32J Compact analytic spaces [Classificació AMS], Classificació AMS::32 Several complex variables and analytic spaces::32C Analytic spaces, Differential geometry, 1-minimal model, differential Galois group, :32 Several complex variables and analytic spaces::32C Analytic spaces [Classificació AMS], Analytic spaces, Gauss-Manin connection, Albanese map

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