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Existence of Dirac eigenvalues of higher multiplicity

Nowaczyk, Nikolai


In this article, we prove that on any compact spin manifold of dimension , there exists a metric, for which the associated Dirac operator has at least one eigenvalue of multiplicity at least two. We prove this by "catching" the desired metric in a subspace of Riemannian metrics with a loop that is not homotopically trivial. We show how this can be done on the sphere with a loop of metrics induced ...


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