The spectrum of twisted Dirac operators on compact flat manifolds
| dc.creator | Miatello, Roberto | |
| dc.creator | Podesta, Ricardo | |
| dc.date | 2003-11-28 | |
| dc.date | 2004-11-05 | |
| dc.date.accessioned | 2026-07-07T05:03:24Z | |
| dc.date.available | 2026-07-07T05:03:24Z | |
| dc.description | Let $M$ be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of $M$, and we derive a formula for the corresponding eta series. In the case of manifolds with holonomy group $\Z_2^k$, we give a very simple expression for the multiplicities of eigenvalues that allows to compute explicitly the $η$-series in terms of values of Riemann-Hurwitz zeta functions, and the $η$-invariant. We give the dimension of the space of harmonic spinors and characterize all $\Z_2^k$-manifolds having asymmetric Dirac spectrum. Furthermore, we exhibit many examples of Dirac isospectral pairs of $\Z_2^k$-manifolds which do not satisfy other types of isospectrality. In one of the main examples, we construct a large family of Dirac isospectral compact flat $n$-manifolds, pairwise non-homeomorphic to each other. | |
| dc.description | 39 pages, revised and expanded version, to appear in TAMS | |
| dc.identifier | https://arxiv.org/abs/math/0312004 | |
| dc.identifier | http://arxiv.org/abs/math/0312004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69403 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58J53 | |
| dc.title | The spectrum of twisted Dirac operators on compact flat manifolds | |
| dc.type | text |