Harmonic spinors on the Davis hyperbolic 4-manifold
Abstract
In this paper we use the G-spin theorem to show that the Davis hyperbolic 4-manifold admits harmonic spinors. This is the first example of a closed hyperbolic 4-manifold that admits harmonic spinors. We also explicitly describe the Spinor bundle of a spin hyperbolic 2- or 4-manifold and show how to calculated the subtle sign terms in the G-spin theorem for an isometry, with isolated fixed points, of a closed spin hyperbolic 2- or 4-manifold.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2018
- DOI:
- 10.48550/arXiv.1803.06382
- arXiv:
- arXiv:1803.06382
- Bibcode:
- 2018arXiv180306382R
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Differential Geometry;
- 53C27
- E-Print:
- 33 pages and 2 figures