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Mathematics > Geometric Topology

Title: 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.
Comments: 33 pages and 2 figures
Subjects: Geometric Topology (math.GT); Differential Geometry (math.DG)
MSC classes: 53C27
Cite as: arXiv:1803.06382 [math.GT]
  (or arXiv:1803.06382v1 [math.GT] for this version)

Submission history

From: John G. Ratcliffe [view email]
[v1] Fri, 16 Mar 2018 19:44:59 GMT (47kb)