Harmonic spinors on the Davis hyperbolic 4-manifold

  title={Harmonic spinors on the Davis hyperbolic 4-manifold},
  author={John G. Ratcliffe and Daniel Ruberman and Steven T. Tschantz},
  journal={Journal of Topology and Analysis},
In this paper, we use the [Formula: see text]-spin theorem to show that the Davis hyperbolic 4-manifold admits harmonic spinors. This is the first example of a closed hyperbolic [Formula: see text]-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 [Formula: see text]-spin theorem for an isometry, with isolated fixed points, of a closed spin hyperbolic 2- or 4-manifold… 

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