# On the existence of harmonic $\mathbf{Z}_2$ spinors

@article{Doan2017OnTE, title={On the existence of harmonic \$\mathbf\{Z\}\_2\$ spinors}, author={Aleksander Doan and Thomas Walpuski}, journal={arXiv: Differential Geometry}, year={2017} }

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

## One Citation

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