Nowaczyk, Nikolai (2016) Existence of Dirac eigenvalues of higher multiplicity. MATHEMATISCHE ZEITSCHRIFT, 284 (1-2). pp. 285-307. ISSN 0025-5874, 1432-1823
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In this article, we prove that on any compact spin manifold of dimension , there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by "catching" the desired metric in a subspace of Riemannian metrics with a loop that is not homotopically trivial. We show how this can be done on the sphere with a loop of metrics induced by a family of rotations. Finally, we transport this loop to an arbitrary manifold (of suitable dimension) by extending some known results about surgery theory on spin manifolds.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LAPLACIAN; OPERATOR; PRESCRIPTION; SPECTRUM; SURGERY; Spin geometry; Dirac operator; Spectral geometry; Dirac spectrum; Prescribing eigenvalues; Surgery theory |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 04 Apr 2019 11:35 |
| Last Modified: | 04 Apr 2019 11:35 |
| URI: | https://pred.uni-regensburg.de/id/eprint/4252 |
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