On the existence of harmonic $\mathbf{Z}_2$ spinors
Abstract
We prove the existence of singular harmonic ${\bf Z}_2$ spinors on $3$manifolds with $b_1 > 1$. The proof relies on a wallcrossing formula for solutions to the SeibergWitten equation with two spinors. The existence of singular harmonic ${\bf Z}_2$ spinors and the shape of our wallcrossing formula shed new light on recent observations made by Joyce regarding Donaldson and Segal's proposal for counting $G_2$instantons.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 arXiv:
 arXiv:1710.06781
 Bibcode:
 2017arXiv171006781D
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 v2: accepted for publication in Journal of Differential Geometry