The Dirac Spectrum (Lecture Notes in Mathematics, 1976) - Softcover

Ginoux, Nicolas

Softcover

ISBN 10: 3642015697 ISBN 13: 9783642015694

Publisher: Springer, 2009

Synopsis

This overview is based on the talk [101] given at the mini-workshop 0648c Dirac operators in di?erential and non-commutative geometry , Mat- matisches Forschungsinstitut Oberwolfach. Intended for non-specialists, it explores the spectrum of the fundamental Dirac operator on Riemannian spin manifolds, including recent research and open problems. No background in spin geometry is required; nevertheless the reader is assumed to be fam- iar with basic notions of di?erential geometry (manifolds, Lie groups, vector and principal bundles, coverings, connections, and di?erential forms). The surveys [41, 132], which themselves provide a very good insight into closed manifolds, served as the starting point. We hope the content of this book re?ects the wide range of ?ndings on and sometimes amazing applications of the spin side of spectral theory and will attract a new audience to the topic. vii Acknowledgements TheauthorwouldliketothanktheMathematischesForschungsinstitutOb- wolfach for its friendly hospitality and stimulating atmosphere, as well as the organizers and all those who participated in the mini-workshop. This s- vey would not have been possible without the encouragement and advice of Christian B¨ ar and Oussama Hijazi as well as the support of the German Research Foundation s Sonderforschungsbereich 647 Raum, Zeit, Materie. Analytische und geometrische Strukturen (Collaborative Research Center 647/Space, Time and Matter. Analytical and Geometric Structures). We would also like to thank Bernd Ammann and Nadine Große for their enlig- eningdiscussions and usefulreferences.

About this title

From the Back Cover

This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, we present the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries. We give examples where the spectrum can be made explicit and present a chapter dealing with the non-compact setting. The methods mostly involve elementary analytical techniques and are therefore accessible for Master students entering the subject. A complete and updated list of references is also included.

Edition details

• Publisher: Springer
• Publication date: 2009
• Language: English
• ISBN 10: 3642015697
• ISBN 13: 9783642015694
• Binding: Paperback
• Number of pages: 171