Harmonic spinors on the Davis hyperbolic 4-manifold

John G. Ratcliffe; Daniel Ruberman; Steven T. Tschantz

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arXiv · 1803.06382

Harmonic spinors on the Davis hyperbolic 4-manifold

John G. Ratcliffe·Daniel Ruberman·Steven T. Tschantz

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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.

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John G. Ratcliffe, Daniel Ruberman, Steven T. Tschantz. 2018-03-16. Harmonic spinors on the Davis hyperbolic 4-manifold. https://arxiv.org/abs/1803.06382

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