Lectures on Kähler Groups

Pierre Py

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English

Princeton University Press
02 July 2025

Differential & Riemannian geometry; Algebraic geometry

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

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

Lectures on Khler 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.

By: Pierre Py
Imprint: Princeton University Press
Country of Publication: United States
Dimensions: Height: 235mm, Width: 156mm,
ISBN: 9780691247151
ISBN 10: 0691247153
Pages: 400
Publication Date: 02 July 2025
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming

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