In this note, we generalize a theorem of Juan Souto on rank and Nielsen equivalence in the fundamental group of a hyperbolic fibered [Formula: see text]-manifold to a large class of hyperbolic group extensions. This includes all hyperbolic extensions of surfaces groups as well as hyperbolic extensions of free groups by convex cocompact subgroups of [Formula: see text].
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Harmonic spinors on the Davis hyperbolic 4-manifold
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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- Award ID(s):
- 1811111
- PAR ID:
- 10323600
- Date Published:
- Journal Name:
- Journal of Topology and Analysis
- Volume:
- 13
- Issue:
- 03
- ISSN:
- 1793-5253
- Page Range / eLocation ID:
- 699 to 737
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S1793525320500247
