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].

中文翻译：

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关于谐波 $Z_2$ 旋量的存在

我们证明了在 b1 > 1 的 3 流形上存在奇异谐波 Z2 旋量。该证明依赖于具有两个旋量的 Seiberg-Witten 方程的解的穿墙公式。奇异谐波 Z2 旋量的存在和我们的穿墙公式的形状为 Joyce [Joy17] 最近关于 Donaldson 和 Segal 的计算 G2-instantons [DS11] 的提议提供了新的见解。