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The Dirac Spectrum

  • Book
  • © 2009

Overview

Authors:
  1. Nicolas Ginoux
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1976)

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Table of contents (8 chapters)

  1. Front Matter

    Pages 1-11
    Download chapter PDF

  2. Basics of spin geometry

    • Nicolas Ginoux
    Pages 1-27

  3. Explicit computations of spectra

    • Nicolas Ginoux
    Pages 29-39

  4. Lower eigenvalue estimates on closed manifolds

    • Nicolas Ginoux
    Pages 41-68

  5. Lower eigenvalue estimates on compact manifolds with boundary

    • Nicolas Ginoux
    Pages 69-75

  6. Upper eigenvalue bounds on closed manifolds

    • Nicolas Ginoux
    Pages 77-92

  7. Prescription of eigenvalues on closed manifolds

    • Nicolas Ginoux
    Pages 93-101

  8. The Dirac spectrum on non-compact manifolds

    • Nicolas Ginoux
    Pages 103-111

  9. Other topics related with the Dirac spectrum

    • Nicolas Ginoux
    Pages 113-129

  10. Back Matter

    Pages 1-32
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Keywords

About this book

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.

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. Álvarez López, Zentralblatt MATH, Vol. 1186, 2010)

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