Dependence of the Dirac spectrum on the spin structure (Q2765841)

The author presents some examples and results related to the influence of the spin structure on the Dirac spectrum of a spin manifold. First he discusses the cases of the 1-spheres, flat tori, 3-dimensional Bieberbach manifolds and spherical space forms, for which the spectrum can be computed explicitly. Another important invariant is the \(\eta\)-invariant and the author studies its dependence on the spin structure. Next the author studies the behavior of the Dirac spectrum under collapse in the case of circle bundles. In this case the spin structure determines the qualitative spectral behavior. In the general case some better estimates for the eigenvalues obtained by using the spin structure could furnish better information about the properties of the Dirac operator. The spinning systole is the relevant spin geometric input. At the final one checks the influence of the spin structure on the continuous spectrum in the case of the noncompact manifold.NEWLINENEWLINEFor the entire collection see [Zbl 0973.00041].