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The fundamental group of Kaehler manifolds
Amorós Torrent, Jaume
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Homology theory
Analytic spaces
Differential geometry
Kaehler group
Malcev algebra
Albanese map
irrational pencil
monodromy in the fundamental group
Gauss-Manin connection
1-minimal model
differential Galois group
Homologia, Teoria d'
Espais analítics
Geometria diferencial
Classificació AMS::14 Algebraic geometry::14F (Co)homology theory
Classificació AMS::32 Several complex variables and analytic spaces::32C Analytic spaces
Classificació AMS::32 Several complex variables and analytic spaces::32J Compact analytic spaces
Classificació AMS::53 Differential geometry::53C Global differential geometry
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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