Overview

"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."

Full Product Details

Author:   Nicolas Ginoux
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2009 ed.
Volume:   1976
Dimensions:   Width: 15.50cm , Height: 0.90cm , Length: 23.50cm
Weight:   0.580kg
ISBN:  

9783642015694

ISBN 10:   3642015697
Pages:   156
Publication Date:   15 June 2009
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Reviews

From the reviews: The book under review is a very complete survey about the spectral properties of the Dirac operator on a Spin manifold. Intended for non-specialists of spin geometry, it is accessible for masters students ! . All throughout the book, classical and recent results are given with complete proofs and an exhaustive bibliography is provided ! this work is useful to researchers in spin geometry and as a reference to learn the Dirac operator. (Julien Roth, Mathematical Reviews, Issue 2010 a) This memory is a survey on the spectral properties of the Dirac operator defined by a spin structure on a Riemannian manifold. I think that it can be used as a valuable guide to get introduced in this subject. The book is self-contained once some basic concepts of differential geometry are known, like vector bundles, Lie groups, principal bundles, connections, curvature, etc. (Jesus A. lvarez Lopez, Zentralblatt MATH, Vol. 1186, 2010)

From the reviews: The book under review is a very complete survey about the spectral properties of the Dirac operator on a Spin manifold. Intended for non-specialists of spin geometry, it is accessible for masters students ! . All throughout the book, classical and recent results are given with complete proofs and an exhaustive bibliography is provided ! this work is useful to researchers in spin geometry and as a reference to learn the Dirac operator. (Julien Roth, Mathematical Reviews, Issue 2010 a)

From the reviews: “The book under review is a very complete survey about the spectral properties of the Dirac operator on a Spin manifold. Intended for non-specialists of spin geometry, it is accessible for masters students … . All throughout the book, classical and recent results are given with complete proofs and an exhaustive bibliography is provided … this work is useful to researchers in spin geometry and as a reference to learn the Dirac operator.” (Julien Roth, Mathematical Reviews, Issue 2010 a) “This memory is a survey on the spectral properties of the Dirac operator defined by a spin structure on a Riemannian manifold. I think that it can be used as a valuable guide to get introduced in this subject. The book is self-contained once some basic concepts of differential geometry are known, like vector bundles, Lie groups, principal bundles, connections, curvature, etc.” (Jesus A. Álvarez López, Zentralblatt MATH, Vol. 1186, 2010)

From the reviews: The book under review is a very complete survey about the spectral properties of the Dirac operator on a Spin manifold. Intended for non-specialists of spin geometry, it is accessible for masters students ... . All throughout the book, classical and recent results are given with complete proofs and an exhaustive bibliography is provided ... this work is useful to researchers in spin geometry and as a reference to learn the Dirac operator. (Julien Roth, Mathematical Reviews, Issue 2010 a) This memory is a survey on the spectral properties of the Dirac operator defined by a spin structure on a Riemannian manifold. I think that it can be used as a valuable guide to get introduced in this subject. The book is self-contained once some basic concepts of differential geometry are known, like vector bundles, Lie groups, principal bundles, connections, curvature, etc. (Jesus A. Alvarez Lopez, Zentralblatt MATH, Vol. 1186, 2010)

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