Translations of Mathematical Monographs 2008; 155 pp; hardcover Volume: 237 ISBN10: 0821839470 ISBN13: 9780821839478 List Price: US$73 Member Price: US$58.40 Order Code: MMONO/237
 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 AtiyahSinger 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
