Mathematical Research Letters

Volume 18 (2011)

Number 5

Harmonic Spinors and Local Deformations of the Metric

Pages: 927 – 936

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n5.a10

Authors

Bernd Ammann (Fakultät für Mathematik, Universität Regensburg 93040 Regensburg, Germany)

Mattias Dahl (Institutionen för Matematik, Kungliga Tekniska Högskolan, 100 44 Stockholm, Sweden)

Emmanuel Humbert (Laboratoire de Mathématiques et Physique Théorique Université de Tours, UFR Sciences et Techniques Parc de Grandmont, 37200 Tour – FRANCE)

Abstract

Let $(M,g)$ be a compact Riemannian spin manifold. The Atiyah–Singerindex theorem yields a lower bound for the dimension of the kernelof the Dirac operator. We prove that this bound can be attained bychanging the Riemannian metric $g$ on an arbitrarily small open set.

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