Operator algebras and geometry
"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 foliation 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 noncommut…
Read More ↓Title Statements
- Full title :Operator algebras and geometry / Hitoshi Moriyoshi, Toshikazu Natsume ; translated by Hitoshi Moriyoshi and Toshikazu Natsume.
Summary
"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 foliation 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."--Jacket.
Read More ↓Edition Statements
- Publication Date:©2008.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©2008.
Notes
"Originally published in Japanese by the Mathematical Society of Japan ... 2001"--Title page verso.
The Physical Object
- Description:viii, 155 pages ; : 27 cm.
Edition Identifiers
- ISBN:9780821839478, 0821839470
- oclc:ocn233485416
- LC Classification:QA326
- Dewey Decimal:512/.556
Table of Contents
C*-algebras -- K-theory -- KK-theory -- Von Neumann algebras -- Cyclic cohomology -- Quantizations and index theory -- Foliation index theorems.
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