Displaying similar documents to “The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces”

Deformation Theory (Lecture Notes)

M. Doubek, Martin Markl, Petr Zima (2007)

Archivum Mathematicum

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First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation between deformations and solutions of the corresponding Maurer-Cartan equation. In Section  we generalize the Maurer-Cartan equation to strongly homotopy Lie algebras and prove the homotopy invariance of the moduli space of solutions of this equation....

The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold

Jonathan Pridham (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups,...