Lectures on K瓣hler Groups

An introduction to the state of the art in the study of K瓣hler groups This book gives an authoritative and up-to-date introduction to the study of fundamental groups of compact K瓣hler manifolds, known as K瓣hler 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 K瓣hler geometry, covering topics such as the actions of K瓣hler groups on spaces of nonpositive curvature, the large-scale geometry of infinite covering spaces of compact K瓣hler 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 K瓣hler group actions on trees; the study of solvable quotients of K瓣hler groups following the works of Arapura, Beauville, Campana, Delzant, and Nori; and Napier and Ramachandran's work characterizing covering spaces of compact K瓣hler manifolds having many ends. It also describes without proof many of the recent breakthroughs in the field. Lectures on K瓣hler 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.