The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4
Let 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 Di...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214179 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4. Bernd Ammann and Mattias Dahl. SIGMA 21 (2025), 102, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862631140371726336 |
|---|---|
| author | Ammann, Bernd Dahl, Mattias |
| author_facet | Ammann, Bernd Dahl, Mattias |
| citation_txt | The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4. Bernd Ammann and Mattias Dahl. SIGMA 21 (2025), 102, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let 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 is connected if is of dimension 2 or 4.
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| first_indexed | 2026-03-14T19:06:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214179 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T19:06:39Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ammann, Bernd Dahl, Mattias 2026-02-20T07:53:03Z 2025 The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4. Bernd Ammann and Mattias Dahl. SIGMA 21 (2025), 102, 18 pages 1815-0659 2020 Mathematics Subject Classification: 53C27; 19K56; 58C40; 58J5 arXiv:2508.01420 https://nasplib.isofts.kiev.ua/handle/123456789/214179 https://doi.org/10.3842/SIGMA.2025.102 Let 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 is connected if is of dimension 2 or 4. Bernd Ammann was supported by the CRC 1085 Higher Invariants (Universität Regensburg) and by SPP 2026 Geometry at infinity, both funded by the DFG. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4 Article published earlier |
| spellingShingle | The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4 Ammann, Bernd Dahl, Mattias |
| title | The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4 |
| title_full | The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4 |
| title_fullStr | The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4 |
| title_full_unstemmed | The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4 |
| title_short | The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4 |
| title_sort | space of dirac-minimal metrics is connected in dimensions 2 and 4 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214179 |
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