Operator algebras and geometry
著者
書誌事項
Operator algebras and geometry
（Translations of mathematical monographs, v. 237）
American Mathematical Society, c2008
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作用素環と幾何学
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注記
Translated from the Japanese
"This work was originally published in Japanese by the Mathematical Society of Japan under the title “作用素環と幾何学" c2001."--T.p. verso
Includes bibliographical references (p. 147-151) and index
内容説明・目次
内容説明
In the early 1980's topologists and geometers for the first time came across unfamiliar words like $C^*$-algebras and von Neumann algebras through the discovery of new knot invariants (by V. F. R. Jones) or through a remarkable result on the relationship between characteristic classes of foliations and the types of certain von Neumann algebras. During the following two decades, a great deal of progress was achieved in studying the interaction between geometry and analysis, in particular in noncommutative geometry and mathematical physics. The present book provides an overview of operator algebra theory and an introduction to basic tools used in noncommutative geometry.The book concludes with applications of operator algebras to Atiyah-Singer type index theorems. The purpose of the book is to convey an outline and general idea of operator algebra theory, to some extent focusing on examples. The book is aimed at researchers and graduate students working in differential topology, differential geometry, and global analysis who are interested in learning about operator algebras.
目次
$C^*$-algebras $K$-theory $KK$-theory Von Neumann algebras Cyclic cohomology Quantizations and index theory Foliation index theorems References Index.
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