Infinite Dimensional Kähler Manifolds (Oberwolfach Seminars)
Contributors: Alan Huckleberry (Editor); Tilmann Wurzbacher (Editor)
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: September 21, 2001
Language: eng
Format: Paperback
Number of pages: 375
ISBN-13: 9783764366025
Subjects: Differential & Riemannian geometry; Topology; Mathematics; Differential Geometry; Science/Mathematics; Geometry - Differential; Geometry; Mathematics / General; complex analysis; group theory
Description: Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.