Surgery and Harmonic Spinors
Bernd Ammann, Mattias Dahl, Emmanuel Humbert

Surgery and Harmonic Spinors (.dvi, .ps,.ps.gz or .pdf)
Adv. Math. 220 no. 2, 523-539 (2009)


Let M be a compact manifold with a fixed spin structure. The Atiyah-Singer index theorem implies that for any Riemannian metric on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending only on M and its spin structure. We show that for generic metrics on M this bound is attained.
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The Paper was written on June 9, 2006
Last update Sept 22, 2008