Zusammenfassung
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 ...
Zusammenfassung
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 by a family of rotations. Finally, we transport this loop to an arbitrary manifold (of suitable dimension) by extending some known results about surgery theory on spin manifolds.
Altmetric