Harmonic spinors on the Davis hyperbolic 4-manifold
Geometric Topology
2018-03-20 v1 Differential Geometry
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.
Cite
@article{arxiv.1803.06382,
title = {Harmonic spinors on the Davis hyperbolic 4-manifold},
author = {John G. Ratcliffe and Daniel Ruberman and Steven T. Tschantz},
journal= {arXiv preprint arXiv:1803.06382},
year = {2018}
}
Comments
33 pages and 2 figures