Buch, Englisch, Band 1976, 156 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 580 g
Reihe: Lecture Notes in Mathematics
Buch, Englisch, Band 1976, 156 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 580 g
Reihe: Lecture Notes in Mathematics
ISBN: 978-3-642-01569-4
Verlag: Springer
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Quantenphysik
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
- Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
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.
