Kã"hler Geometry of Loop Spaces
暫譯: 迴圈空間的卡赫幾何學

Sergeev, Armen

  • 出版商: World Scientific Pub
  • 出版日期: 2010-05-31
  • 售價: $1,340
  • 貴賓價: 9.5$1,273
  • 語言: 英文
  • 頁數: 228
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 4931469604
  • ISBN-13: 9784931469600
  • 相關分類: 數學
  • 海外代購書籍(需單獨結帳)

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商品描述

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

商品描述(中文翻譯)

在本書中,我們研究三個重要的無限維 Kähler 流形類別——緊李群的迴圈空間、迴圈空間上的複結構的 Teichmüller 空間,以及希爾伯特空間的 Grassmannian。這些流形各自擁有豐富的 Kähler 幾何,這部分內容在本書的第一部分中進行探討,並且可以被視為一個範疇中的普遍對象,包含了所有的有限維對應物。另一方面,這些流形與弦理論密切相關。這激發了我們對其幾何量子化的興趣,該內容在本書的第二部分中呈現,並簡要回顧了有限維 Kähler 流形的幾何量子化。本書附有一章介紹無限維 Fréchet 流形和 Fréchet 李群的基本概念。它也可以作為無限維複流形 Kähler 幾何的易讀入門,特別關注上述三個特定類別。對於從事無限維複流形研究的數學家和處理弦理論的物理學家來說,這本書可能會很有趣。本書由日本數學會出版,並由世界科學出版社在所有市場發行。