AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

Operator Algebras and Geometry
Hitoshi Moriyoshi, Keio University, Yokohama, Japan, and Toshikazu Natsume, Nagoya Institute of Technology, Japan
cover
SEARCH THIS BOOK:

Translations of Mathematical Monographs
2008; 155 pp; hardcover
Volume: 237
ISBN-10: 0-8218-3947-0
ISBN-13: 978-0-8218-3947-8
List Price: US$69
Member Price: US$55.20
Order Code: MMONO/237
[Add Item]

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.

Readership

Graduate students and research mathematicians interested in applications of functional analysis to geometry and topology.

Table of Contents

  • \(C^*\)-algebras
  • \(K\)-theory
  • \(KK\)-theory
  • Von Neumann algebras
  • Cyclic cohomology
  • Quantizations and index theory
  • Foliation index theorems
  • References
  • Index
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia