非退化$\boldsymbol{\frac{\boldsymbol{Z}}{\boldsymbol{2}Z}}$调和旋子的通用模空间
The universal moduli space of non-degenerate $\mathbb{Z}/2\mathbb{Z}$ harmonic spinors
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中文总结 AI 辅助
本文为非退化$\boldsymbol{\frac{\boldsymbol{Z}}{\boldsymbol{2}Z}}$调和旋子的通用模空间赋予驯服Fréchet流形结构，证明其投影映射为一致Fredholm，在统一框架下重现了Donaldson等人的早期工作。
中文摘要 AI 辅助
本文为非退化$\boldsymbol{\frac{\boldsymbol{Z}}{\boldsymbol{2}Z}}$调和旋子的通用模空间赋予了驯服Fréchet流形的结构，并证明其到参数空间的投影映射是一致Fredholm的，该结果在统一框架下重现了Donaldson、Parker和Takahashi的早期工作。
英文摘要
This article equips the universal moduli spaces of non-degenerate $\mathbb{Z}/2\mathbb{Z}$ harmonic spinors and eigenspinors with tame Fréchet manifold structures and proves that their natural projections to the corresponding parameter spaces are uniformly Fredholm. A unified construction yields the deformation theories of harmonic spinors and eigenspinors in dimension three and of chiral harmonic spinors in dimension four, recovering earlier work of Donaldson, Parker, and Takahashi. As an application, a deformation theory for non-degenerate $\mathbb{Z}/2\mathbb{Z}$ harmonic self-dual $2$-forms in dimension four is established.
