Ammann, Bernd and Dahl, Mattias (2025) The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 21: 102. ISSN 1815-0659
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Let M be a closed connected spin manifold. Index theory provides a topological lower bound on the dimension of the kernel of the Dirac operator which depends on the choice of Riemannian metric. Riemannian metrics for which this bound is attained are called Dirac-minimal. We show that the space of Dirac-minimal metrics on M is connected if M is of dimension 2 or 4.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SPIN; Dirac operator; Atiyah-Singer index theorem; generic Riemannian metrics; minimal kernel |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Aug 2026 05:18 |
| Last Modified: | 12 Aug 2026 05:18 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66206 |
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