Lectures on Kähler Groups

by Pierre Py

Overview

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

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

Lectures on Kähler 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.

Product Details

ISBN-13:	9780691247168
Publisher:	Princeton University Press
Publication date:	03/25/2025
Series:	Princeton Mathematical Series , #53
Sold by:	Barnes & Noble
Format:	eBook
Pages:	400
File size:	4 MB

About the Author

Pierre Py is a CNRS researcher at the Université Grenoble Alpes in France.

What People are Saying About This

From the Publisher

“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 Kähler manifolds.”—János Kollár, 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 Kähler 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 Kähler groups on trees and other non-positively curved spaces, and extensively describes the study of the first cohomology groups attached to the characters of Kähler groups.”—Benoît Claudon, University of Rennes