The Dirac operator under collapse to a smooth limit space
- Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B.
| Author details: | Saskia RoosORCiD |
|---|---|
| DOI: | https://doi.org/10.1007/s10455-019-09691-8 |
| ISSN: | 0232-704X |
| ISSN: | 1572-9060 |
| Title of parent work (English): | Annals of global analysis and geometry |
| Publisher: | Springer |
| Place of publishing: | Dordrecht |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/10/25 |
| Publication year: | 2019 |
| Release date: | 2021/06/03 |
| Tag: | Collapse; Dirac operator; Spin geometry |
| Volume: | 57 |
| Issue: | 1 |
| Number of pages: | 31 |
| First page: | 121 |
| Last Page: | 151 |
| Funding institution: | Hausdorff Research Institute for Mathematics in Bonn |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
