The Dirac spectrum

Author(s)

    • Ginoux, Nicolas

Bibliographic Information

The Dirac spectrum

Nicolas Ginoux

(Lecture notes in mathematics, 1976)

Springer, c2009

  • : pbk

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Note

Bibliography: p. 145-154

Includes index

Description and Table of Contents

Description

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.

Table of Contents

Basics of spin geometry.- Explicit computations of spectra.- Lower eigenvalue estimates on closed manifolds.- Lower eigenvalue estimates on compact manifolds with boundary.- Upper eigenvalue bounds on closed manifolds.- Prescription of eigenvalues on closed manifolds.- The Dirac spectrum on non-compact manifolds.- Other topics related with the Dirac spectrum.

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Details

  • NCID
    BA90386667
  • ISBN
    • 9783642015694
  • LCCN
    2009926184
  • Country Code
    gw
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Berlin ; London
  • Pages/Volumes
    xv, 156 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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