Kã"hler Geometry of Loop Spaces (Mathematical Society of Japan Memoirs #23) (Paperback)

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In this book we study three important classes of infinite-dimensional K hler manifolds -- loop spaces of compact Lie groups, Teichm ller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces. Each of these manifolds has a rich K hler geometry, considered in the first part of the book, and may be considered as a universal object in a category, containing all its finite-dimensional counterparts.On the other hand, these manifolds are closely related to string theory. This motivates our interest in their geometric quantization presented in the second part of the book together with a brief survey of geometric quantization of finite-dimensional K hler manifolds.The book is provided with an introductory chapter containing basic notions on infinite-dimensional Frechet manifolds and Frechet Lie groups. It can also serve as an accessible introduction to K hler geometry of infinite-dimensional complex manifolds with special attention to the aforementioned three particular classes.It may be interesting for mathematicians working with infinite-dimensional complex manifolds and physicists dealing with string theory.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets.

Product Details
ISBN: 9784931469600
ISBN-10: 4931469604
Publisher: Mathematical Society of Japan
Publication Date: May 31st, 2010
Pages: 228
Language: English
Series: Mathematical Society of Japan Memoirs