The space of Dirac-minimal metrics is connected in dimensions 2 and 4
by
Bernd Ammann, Mattias Dahl
The space of Dirac-minimal metrics is connected in dimensions 2 and 4,
Preprint version (pdf)
Abstract
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.
53C27 (Primary), 19K56, 58C40, 58J50 (Secondary)
Keywords
Dirac operator; Atiyah-Singer index theorem; generic Riemannian metrics; minimal kernel
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Last update of this page 24.11.2025
The paper was originally written on 2.8.2025