This book gives an authoritative and up-to-date introduction to the study of fundamental groups of compact K盲hler manifolds, known as K盲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盲hler geometry, covering topics such as the actions of K盲hler groups on spaces of nonpositive curvature, the large-scale geometry of infinite covering spaces of compact K盲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鈥檚 description of K盲hler group actions on trees; the study of solvable quotients of K盲hler groups following the works of Arapura, Beauville, Campana, Delzant, and Nori; and Napier and Ramachandran鈥檚 work characterizing covering spaces of compact K盲hler manifolds having many ends. It also describes without proof many of the recent breakthroughs in the field.
Lectures on K盲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.
Pierre Py is a CNRS researcher at the Universit茅 Grenoble Alpes in France.
“The book is the first systematic treatment of this active research area in thirty years. Besides treating all the major research directions, it also provides succinct introductions to seemingly unrelated fields that proved to be essential. It will be an indispensable book for anyone interested in learning about the latest results and questions about fundamental groups of K盲hler manifolds.”—J谩nos Koll谩r, Princeton University
“Py’s book is the first systematic treatment of this subject as a whole and is written in such a way as to be maximally useful to someone interested in any part of it. Results are presented cleanly and elegantly, with technical details relegated to the extensive appendixes. This is a book every geometer will want on their shelf.”—Danny Calegari, University of Chicago
“Py provides an informative and well-written introduction to the study of K盲hler groups, centering on methods from differential geometry and geometric group theory and covering a number of recent topics in this area. I certainly learned many new things from this book.”—Donu Arapura, Purdue University
“A significant contribution. This book gives an up-to-date account of the actions of K盲hler groups on trees and other non-positively curved spaces, and extensively describes the study of the first cohomology groups attached to the characters of K盲hler groups.”—Beno卯t Claudon, University of Rennes
