Lectures on Kähler Groups (eBook)

Pierre Py (Autor)

eBook Download: PDF

2025
399 Seiten
Princeton University Press (Verlag)
978-0-691-24716-8 (ISBN)

Infos

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

Produkt-Details

• Erscheint lt. Verlag: 25.3.2025
• Reihe/Serie: Princeton Mathematical Series
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: amenability • Bieri-Neumann-Strebel invariant • Castelnuovo-de Franchis theorem • ends of spaces • fundamental group • geometric group theory • groups acting on trees • harmonic maps • Hodge Theory • Kähler groups • Kähler manifolds • L ^2 cohomology • lattices in Lie groups • non-abelian Hodge theory • Nonpositive curvature • pluriharmonic map • plurisubharmonic function. • Potential Theory
• ISBN-10: 0-691-24716-1 / 0691247161
• ISBN-13: 978-0-691-24716-8 / 9780691247168