**Proceedings of Symposia in Pure Mathematics**

Volume: 81;
2010;
249 pp;
Hardcover

MSC: Primary 81; 55; 46;

Print ISBN: 978-0-8218-4887-6

Product Code: PSPUM/81

List Price: $67.00

Individual Member Price: $53.60

**Electronic ISBN: 978-0-8218-9389-0
Product Code: PSPUM/81.E**

List Price: $67.00

Individual Member Price: $53.60

# Superstrings, Geometry, Topology, and \(C^{*}\)-algebras

Share this page *Edited by *
*Robert S. Doran; Greg Friedman; Jonathan Rosenberg*

This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18–22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in \(K\)-homology and twisted \(K\)-homology, Yang-Mills gauge theory and connections with non-commutative geometry, Landau-Ginzburg models, \(C^*\)-algebraic non-commutative geometry and ties to quantum physics and topology, the rational homotopy type of the group of unitary elements in an Azumaya algebra, and functoriality properties in the theory of \(C^*\)-crossed products and fixed point algebras for proper actions. An introduction, written by Jonathan Rosenberg, provides an instructive overview describing common themes and how the various papers in the volume are interrelated and fit together. The rich diversity of papers appearing in the volume demonstrates the current interplay between superstring theory, geometry/topology, and non-commutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.

#### Table of Contents

# Table of Contents

## Superstrings, Geometry, Topology, and $C^{*}$-algebras

- Contents v6 free
- Preface vii8 free
- Conference Attendees xi12 free
- Conference Speakers xiii14 free
- Introduction 116 free
- Functoriality of Rieffel’s Generalised Fixed-Point Algebras for Proper Actions 924
- Twists of K-theory and TMF 2742
- Division Algebras and Supersymmetry I 6580
- K-homology and D-branes 8196
- Riemann-Roch and Index Formulae in Twisted K-theory 95110
- Noncommutative Principal Torus Bundles via Parametrised Strict Deformation Quantization 133148
- A Survey of Noncommutative Yang-Mills Theory for Quantum Heisenberg Manifolds 149164
- From Rational Homotopy to K-Theory for Continuous Trace Algebras 165180
- Distances between Matrix Algebras that Converge to Coadjoint Orbits 173188
- Geometric and Topological Structures Related to M-branes 181196
- Landau-Ginzburg Models, Gerbes, and Kuznetsov’s Homological Projective Duality 237252

#### Readership

Graduate students and research mathematicians interested in the relations between mathematical physics and various areas of pure mathematics.