# 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)

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.
53C27 (Primary) 55N22, 57R65 (Secondary)
### Typos 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}.
- On page 10004, line 7, the spinors should be restricted to the boundary ∂ N instead of N.

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The Paper was written on 25.3.2009

Last update 26.6.2023