Kähler Geometry of Loop Spaces (Mathematical Society of Japan Memoirs)

In this book we study three important classes of infinite-dimensional Kähler manifolds — loop spaces of compact Lie groups, Teichmüller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces. Each of these manifolds has a rich Kähler 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. Studies three important classes of infinite-dimensional Kahler manifolds - loop spaces of compact Lie groups, Teichmuller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces. The book is provided with an introductory chapter containing basic notions on infinite-dimensional Frechet manifolds and Frechet Lie groups. Title and Copyright Pages.pdf Contents Foreword Part I. Preliminary Concepts Part II. Loop Spaces of Compact Lie Groups Part III. Spaces of Complex Structures Part IV. Quantization of Finite-Demensional Kähler Manifolds Part V. Quantization of Loop Spaces Bibliography Index Armen Sergeev. Includes Bibliographical References (p. 203-207) And Index.