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March 2021 On the existence of harmonic $Z_2$ spinors
Aleksander Doan, Thomas Walpuski
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J. Differential Geom. 117(3): 395-449 (March 2021). DOI: 10.4310/jdg/1615487003

Abstract

We prove the existence of singular harmonic $\mathbf{Z}_2$ spinors on $3$‑manifolds with $b_1 \gt 1$. The proof relies on a wall-crossing formula for solutions to the Seiberg–Witten equation with two spinors. The existence of singular harmonic $\mathbf{Z}_2$ spinors and the shape of our wall-crossing formula shed new light on recent observations made by Joyce [Joy17] regarding Donaldson and Segal’s proposal for counting $G_2$-instantons [DS11].

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Aleksander Doan. Thomas Walpuski. "On the existence of harmonic $Z_2$ spinors." J. Differential Geom. 117 (3) 395 - 449, March 2021. https://doi.org/10.4310/jdg/1615487003

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Received: 4 December 2017; Published: March 2021
First available in Project Euclid: 11 March 2021

Digital Object Identifier: 10.4310/jdg/1615487003

Rights: Copyright © 2021 Lehigh University

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Vol.117 • No. 3 • March 2021
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