**CBMS Regional Conference Series in Mathematics**

Volume: 111;
2009;
110 pp;
Softcover

MSC: Primary 81;
Secondary 19; 46; 58; 55; 14; 53

**Print ISBN: 978-0-8218-4922-4
Product Code: CBMS/111**

List Price: $38.00

Individual Price: $30.40

**Electronic ISBN: 978-1-4704-1569-3
Product Code: CBMS/111.E**

List Price: $35.00

AMS Member Price: $28.00

MAA Member Price: $31.50

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#### Supplemental Materials

# Topology, \(C^*\)-Algebras, and String Duality

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*Jonathan Rosenberg*

A co-publication of the AMS and CBMS

String theory is the leading candidate for a physical theory that
combines all the fundamental forces of nature, as well as the principles
of relativity and quantum mechanics, into a mathematically elegant
whole. The mathematical tools used by string theorists are highly
sophisticated, and cover many areas of mathematics. As with the birth
of quantum theory in the early 20th century, the mathematics has
benefited at least as much as the physics from the collaboration. In
this book, based on CBMS lectures given at Texas Christian University,
Rosenberg describes some of the most recent interplay between string
dualities and topology and operator algebras.

The book is an interdisciplinary approach to duality symmetries in
string theory. It can be read by either mathematicians or theoretical
physicists, and involves a more-or-less equal mixture of algebraic
topology, operator algebras, and physics. There is also a bit of
algebraic geometry, especially in the last chapter. The reader is
assumed to be somewhat familiar with at least one of these four
subjects, but not necessarily with all or even most of them. The main
objective of the book is to show how several seemingly disparate
subjects are closely linked with one another, and to give readers an
overview of some areas of current research, even if this means that not
everything is covered systematically.

A co-publication of the AMS and CBMS.

#### Readership

Graduate students and research mathematicians interested in mathematical physics, particularly string theory; topology; C*-algebras.

#### Reviews & Endorsements

Rosenberg manages to state the main results, give the most illuminating examples and explain the most important ideas of the proofs. It can be highly recommended as a concise introduction to the subjects [discussed in this book].

-- Mathematical Reviews

#### Table of Contents

# Table of Contents

## Topology, $C^{*}$-Algebras, and String Duality

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Introduction and motivation 110 free
- 𝐾-theory and its relevance to physics 1322 free
- A few basics of 𝐶*-algebras and crossed products 2534
- Continuous-trace algebras and twisted 𝐾-theory 3746
- More on crossed products and their 𝐾-theory 4756
- The topology of T-duality and the Bunke-Schick construction 5564
- T-duality via crossed products 6372
- Higher-dimensional T-duality via topological methods 7180
- Higher-dimensional T-duality via 𝐶*-algebraic methods 7786
- Advanced topics and open problems 8594
- Bibliography 95104
- Notation and symbols 103112
- Index 107116 free
- Back Cover Back Cover1122