The universal moduli space of non-degenerate $\mathbb{Z}/2\mathbb{Z}$ harmonic spinors

Abstract

This article equips the universal moduli spaces of non-degenerate $\mathbb{Z}/2\mathbb{Z}$ harmonic spinors with the structure of a tame Fréchet manifold and proves that the projection map to the parameter space is uniformly Fredholm. This recovers earlier work of Donaldson, Parker, and Takahashi in a unified framework.