Harmonic spinors and local deformations of the metric

Mathematics – Differential Geometry

Scientific paper

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minor changes, to appear in Mathematical Research Letters

Scientific paper

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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