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Topology, $C^*$-Algebras, and String Duality

Jonathan Rosenberg University of Maryland, College Park, MD
A co-publication of the AMS and CBMS
Available Formats:
Softcover 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 MAA Member Price:$31.50
AMS Member Price: $28.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$57.00
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Topology, $C^*$-Algebras, and String Duality
Jonathan Rosenberg University of Maryland, College Park, MD
A co-publication of the AMS and CBMS
Available Formats:
 Softcover 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 MAA Member Price:$31.50 AMS Member Price: $28.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$57.00
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1112009; 110 pp
MSC: Primary 81; Secondary 19; 46; 58; 55; 14; 53;

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.

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

• Chapters
• Chapter 1. Introduction and motivation
• Chapter 2. $K$-theory and its relevance to physics
• Chapter 3. A few basics of $C$*-algebras and crossed products
• Chapter 4. Continuous-trace algebras and twisted $K$-theory
• Chapter 5. More on crossed products and their $K$-theory
• Chapter 6. The topology of T-duality and the Bunke-Schick construction
• Chapter 7. T-duality via crossed products
• Chapter 8. Higher-dimensional T-duality via topological methods
• Chapter 9. Higher-dimensional T-duality via $C$*-algebraic methods
• Chapter 10. Advanced topics and open problems

• Reviews

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 1112009; 110 pp
MSC: Primary 81; Secondary 19; 46; 58; 55; 14; 53;

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.

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

• Chapters
• Chapter 1. Introduction and motivation
• Chapter 2. $K$-theory and its relevance to physics
• Chapter 3. A few basics of $C$*-algebras and crossed products
• Chapter 4. Continuous-trace algebras and twisted $K$-theory
• Chapter 5. More on crossed products and their $K$-theory
• Chapter 6. The topology of T-duality and the Bunke-Schick construction
• Chapter 7. T-duality via crossed products
• Chapter 8. Higher-dimensional T-duality via topological methods
• Chapter 9. Higher-dimensional T-duality via $C$*-algebraic methods
• Chapter 10. Advanced topics and open problems
• 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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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