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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 81; 2010; 249 ppMSC: Primary 81; 55; 46;
This volume contains the proceedings of an NSFCBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18–22, 2009. The papers, written especially for this volume by wellknown 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 Dbrane charges in \(K\)homology and twisted \(K\)homology, YangMills gauge theory and connections with noncommutative geometry, LandauGinzburg models, \(C^*\)algebraic noncommutative 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 noncommutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.
ReadershipGraduate students and research mathematicians interested in the relations between mathematical physics and various areas of pure mathematics.

Table of Contents

Articles

Jonathan Rosenberg  Introduction [ MR 2681755 ]

Astrid an Huef, Iain Raeburn and Dana P. Williams  Functoriality of Rieffel’s generalised fixedpoint algebras for proper actions [ MR 2681756 ]

Matthew Ando, Andrew J. Blumberg and David Gepner  Twists of $K$theory and TMF [ MR 2681757 ]

John C. Baez and John Huerta  Division algebras and supersymmetry I [ MR 2681758 ]

Paul Baum  $K$homology and Dbranes [ MR 2681759 ]

Alan L. Carey and BaiLing Wang  RiemannRoch and index formulae in twisted $K$theory [ MR 2681760 ]

Keith C. Hannabuss and Varghese Mathai  Noncommutative principal torus bundles via parametrised strict deformation quantization [ MR 2681761 ]

Sooran Kang  A survey of noncommutative YangMills theory for quantum Heisenberg manifolds [ MR 2681762 ]

John R. Klein, Claude L. Schochet and Samuel B. Smith  From rational homotopy to $K$theory for continuous trace algebras [ MR 2681763 ]

Marc A. Rieffel  Distances between matrix algebras that converge to coadjoint orbits [ MR 2681764 ]

Hisham Sati  Geometric and topological structures related to Mbranes [ MR 2681765 ]

Eric Sharpe  LandauGinzburg models, gerbes, and Kuznetsov’s homological projective duality [ MR 2681766 ]


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This volume contains the proceedings of an NSFCBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18–22, 2009. The papers, written especially for this volume by wellknown 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 Dbrane charges in \(K\)homology and twisted \(K\)homology, YangMills gauge theory and connections with noncommutative geometry, LandauGinzburg models, \(C^*\)algebraic noncommutative 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 noncommutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.
Graduate students and research mathematicians interested in the relations between mathematical physics and various areas of pure mathematics.

Articles

Jonathan Rosenberg  Introduction [ MR 2681755 ]

Astrid an Huef, Iain Raeburn and Dana P. Williams  Functoriality of Rieffel’s generalised fixedpoint algebras for proper actions [ MR 2681756 ]

Matthew Ando, Andrew J. Blumberg and David Gepner  Twists of $K$theory and TMF [ MR 2681757 ]

John C. Baez and John Huerta  Division algebras and supersymmetry I [ MR 2681758 ]

Paul Baum  $K$homology and Dbranes [ MR 2681759 ]

Alan L. Carey and BaiLing Wang  RiemannRoch and index formulae in twisted $K$theory [ MR 2681760 ]

Keith C. Hannabuss and Varghese Mathai  Noncommutative principal torus bundles via parametrised strict deformation quantization [ MR 2681761 ]

Sooran Kang  A survey of noncommutative YangMills theory for quantum Heisenberg manifolds [ MR 2681762 ]

John R. Klein, Claude L. Schochet and Samuel B. Smith  From rational homotopy to $K$theory for continuous trace algebras [ MR 2681763 ]

Marc A. Rieffel  Distances between matrix algebras that converge to coadjoint orbits [ MR 2681764 ]

Hisham Sati  Geometric and topological structures related to Mbranes [ MR 2681765 ]

Eric Sharpe  LandauGinzburg models, gerbes, and Kuznetsov’s homological projective duality [ MR 2681766 ]