Lectures on Kaehler Groups

An introduction to the state of the art in the study of Kaehler groups

This book gives an authoritative and up-to-date introduction to the study of fundamental groups of compact Kaehler manifolds, known as Kaehler groups. Approaching the subject from the perspective of a geometric group theorist, Pierre Py equips readers with the necessary background in both geometric group theory and Kaehler geometry, covering topics such as the actions of Kaehler groups on spaces of nonpositive curvature, the large-scale geometry of infinite covering spaces of compact Kaehler manifolds, and the topology of level sets of pluriharmonic functions.

Presenting the most important results from the past three decades, the book provides graduate students and researchers with detailed original proofs of several central theorems, including Gromov and Schoen's description of Kaehler group actions on trees; the study of solvable quotients of Kaehler groups following the works of Arapura, Beauville, Campana, Delzant, and Nori; and Napier and Ramachandran's work characterizing covering spaces of compact Kaehler manifolds having many ends. It also describes without proof many of the recent breakthroughs in the field.

Lectures on Kaehler Groups also gives, in eight appendixes, detailed introductions to such topics as the study of ends of groups and spaces, groups acting on trees and Hilbert spaces, potential theory, and L2 cohomology on Riemannian manifolds.