The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Ammann, Bernd, Dahl, Mattias
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214179
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Space of Dirac-Minimal Metrics is Connected in Dimensions 2 and 4. Bernd Ammann and Mattias Dahl. SIGMA 21 (2025), 102, 18 pages

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...