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
Datum:2025
Hauptverfasser: Ammann, Bernd, Dahl, Mattias
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2025
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
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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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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.
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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
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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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