Harmonic spinors and local deformations of the metric

Abstract

Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.

minor changes, to appear in Mathematical Research Letters

References in corpus (2)

• Surgery and Harmonic Spinors
• The invertible double of elliptic operators

Cited by in corpus (7)

• Dirac-harmonic maps from index theory
• The Cauchy problems for Einstein metrics and parallel spinors
• Dirac eigenspinors for generic metrics
• Mass endomorphism, surgery and perturbations
• Spectral asymmetry of the massless Dirac operator on a 3-torus
• $L^p$-spectrum of the Dirac operator on products with hyperbolic spaces
• Homotopy equivalence of spaces of metrics with invertible Dirac operator