
Operator Algebras and Geometry
American Mathematical Society (Publisher)
Will be published approx. on 30. January 2009
Book
Hardback
155 pages
978-0-8218-3947-8 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Professional and scholarly
Weight
460 gr
ISBN-13
978-0-8218-3947-8 (9780821839478)
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Schweitzer Classification
Content
$C^*$-algebras $K$-theory $KK$-theory Von Neumann algebras Cyclic cohomology Quantizations and index theory Foliation index theorems References Index.