**Translations of Mathematical Monographs**

2008;
155 pp;
Hardcover

MSC: Primary 46;
**Print ISBN: 978-0-8218-3947-8
Product Code: MMONO/237**

List Price: $73.00

AMS Member Price: $58.40

MAA member Price: $65.70

#### Supplemental Materials

# Operator Algebras and Geometry

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*Hitoshi Moriyoshi; Toshikazu Natsume*

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.