Surgery and Harmonic Spinors

Abstract

Let M be a compact manifold with a fixed spin structure χ. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending only on M and χ. We show that for generic metrics on M this bound is attained.

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References in corpus (1)

• Dirac operators on manifolds with periodic ends

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