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Lecture Notes in Mathematics

Introduction to Symplectic Dirac Operators

Authors: Habermann, Katharina, Habermann, Lutz

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About this book

One of the basic ideas in differential geometry is that the study of analytic properties of certain differential operators acting on sections of vector bundles yields geometric and topological properties of the underlying base manifold. Symplectic spinor fields are sections in an L^2-Hilbert space bundle over a symplectic manifold and symplectic Dirac operators, acting on symplectic spinor fields, are associated to the symplectic manifold in a very natural way. Hence they may be expected to give interesting applications in symplectic geometry and symplectic topology. These symplectic Dirac operators are called Dirac operators, since they are defined in an analogous way as the classical Riemannian Dirac operator known from Riemannian spin geometry. They are called symplectic because they are constructed by use of the symplectic setting of the underlying symplectic manifold. This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.

About the authors

Katharina Habermann is awarded by the "Gerhard Hess Preis 2000" – a research prize of the German Research Foundation (DFG) for excellent young researchers.

Reviews

From the reviews:

"The book starts with an introductory chapter which contains the background on symplectic spinors … . The book will be of interest to researchers working on symplectic geometry and /or symplectic topology, and in physicists interested to quantization." (Aurel Bejancu, Zentralblatt MATH, Vol. 1102 (4), 2007)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-540-33421-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-540-33420-0
  • with online files
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Symplectic Dirac Operators
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1887
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-33421-7
DOI
10.1007/b138212
Softcover ISBN
978-3-540-33420-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 125
Topics

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