Surgery and harmonic spinors

• Autores: Bernd Ammann, Mattias Dahl, Emmanuel Humbert
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 220, Nº 2, 2009, págs. 523-539
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.09.013
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• Resumen

  • Let M be a compact spin manifold with a chosen 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 the spin structure. We show that for generic metrics on M this bound is attained.