The fundamental group of Kaehler manifolds

Abstract

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.