Mathematical Research Letters
Volume 18 (2011)
Harmonic Spinors and Local Deformations of the Metric
Pages: 927 – 936
Let $(M,g)$ be a compact Riemannian spin manifold. The Atiyah–Singerindex theorem yields a lower bound for the dimension of the kernelof the Dirac operator. We prove that this bound can be attained bychanging the Riemannian metric $g$ on an arbitrarily small open set.
Published 28 October 2011