Operator algebras and geometry
By: Hitoshi Moriyoshi, Toshikazu Natsume ; translated by Hitoshi Moriyoshi, Toshikazu Natsume.
Contributors: Natsume, Toshikazu.
Series: Translation of mathematical monographs -- v. 237
Publisher: American Mathematical Society
Published: 2008
Place of publication: Providence, R.I
Language: eng
Number of pages: 155
ISBN-13: 9780821839478
Subjects: Operator algebras; Geometry
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 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.
Notes: Includes bibliographical references and index.