Harmonic spinors and local deformations of the metric
by
Bernd Ammann, Mattias Dahl, Emmanuel Humbert


Harmonic spinors and local deformations of the metric (.pdf)
Math. Res. Lett. 18, 927-936 (2011)

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.

Mathematics Subject Classification

53C27 (Primary) 55N22, 57R65 (Secondary)

Typo in printed version

In the proof of Lemma A.1, one has to replace twice σ-1(B) by σ(B-1) or equivalently by σ(B)-1.
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The Paper was written on 25.3.2009
Last update 10.6.2011