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Harmonic spinors and local deformations of the metric

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Ammann, Bernd ; Dahl, Matthias ; Humbert, Emmanuel
Date of publication of this fulltext: 12 Feb 2010 10:57


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.

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