On the Malcev completion of Kähler groups

Abstract

Restrictions are placed on the presentation and holonomy algebra of a Kähler group. Let $X$ be compact Kähler. It is known that the formality of $X$, its Albanese map and the Hodge structure of $H^{\ast }(X)$ impose restrictions on the holonomy algebra of ${\pi }_{1}X$. We derive further restrictions from Sullivan's 1-minimal model. An effective algorithm is given to compute the holonomy algebra of a group from a presentation. Some very strong restrictions on Kähler groups with few defining relations are obtained.

arXiv commentAMS-TeX v. 2.0, 17 pages

Cited by in corpus (2)

• Three-manifolds and Kaehler groups
• Cohomological restrictions on Kahler groups