Proceedings of the summer school and workshop : Dirac operators : yesterday and today : CAMS-AUB, Lebanon : August 27 - September 7, 2001
著者
書誌事項
Proceedings of the summer school and workshop : Dirac operators : yesterday and today : CAMS-AUB, Lebanon : August 27 - September 7, 2001
（Conference proceedings and lecture notes in Geometry and topology）
International Press, c2005
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Dirac operators : yesterday and today : CAMS-AUB, Lebanon
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注記
Includes bibliographical references (p. 293-304)
内容説明・目次
内容説明
This volume represents the proceedings of a summer school and workshop on Dirac operators held at the American University of Beirut in 2001. An introduction to all necessary background material to begin research in Dirac operators is presented including elementary differential geometry, Clifford algebras, Lie groups, special geometries, leading to a presentation of the fundamental role of Dirac operators in the Atiyah-Singer Index Theorem and particle physics. More advanced topics are presented in the proceedings of the workshop where, for example, topics on the spectrum of Dirac operators, pseudo-Riemannian geometry, and first eigenvalue estimates are presented. This book is suitable for self-study by students and non-experts as a panorama on Dirac operators, but also contains, for experts, an outstanding bibliography on the subject.
目次
- Part 1. Summer School
- * H. B. Lawson, Jr. -- Introduction to the Dirac operator
- * C. Bar -- Introduction to differential manifolds
- * O. Hijazi -- Clifford algebras and spinor representations
- * J.-P. Bourguignon -- A brief introduction to Riemannian and spinorial geometries
- * R. Bryant -- Holonomy and special geometries
- * R. J. Stanton -- A visit to representation theory
- * H. B. Lawson, Jr. -- The Atiyah-Singer index theorem and applications
- * C. Bar -- The spectrum of the Dirac operator
- * T. Branson -- Conformal structure and spin geometry
- * A. H. Chamseddine -- A brief introduction to particle interactions
- Part 2. Workshop
- * B. Ammann -- Ambient Dirac eigenvalue estimates and the Willmore functional
- * H. Baum and F. Leitner -- The geometric structure of Lorentzian manifolds with twistor spinors in low dimension
- * F. El Chami -- Geometric spectrum of isospectral spherical space forms
- * A. El Kacimi -- Towards a basic index theory
- * N. Ginoux -- Reilly-type spinorial inequalities
- * S. Montiel -- Dirac operators and hypersurfaces
- * A. Moroianu -- From Kirchberg's inequality to the Goldberg conjecture.
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