We prove the existence of singular harmonic Z₂ spinors on $3$‑manifolds with b₁ > 1. The proof relies on a wall-crossing formula for solutions to the Seiberg–Witten equation with two spinors. The existence of singular harmonic Z₂ 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 G₂-instantons [DS11].
No takes yet. Share an insight, caveat, or question.
A 2021 study studied this question.