AI 中文总结
该文为非紧复解析Calabi-Yau 4-流形构建模叠的典范定向理论，得到所有PT对模空间的典范族定向，为证明GW/PT对应奠定基础。
AI 中文摘要
我们通过扩展和推广 Joyce 与 Upmeier 的工作以及 Bojko 的工作，为非紧复解析 Calabi-Yau 4-流形上的模叠构建了一个凝聚的拓扑定向理论。作为结果，我们特别得到了所有 Pandharipande-Thomas 对的模空间的典范族定向。我们的证明使用了表示 KU- 和 KO-理论的映射空间的代数拓扑，以及李群 E_8 和令人惊讶的 HSpin(16) 的一些性质。这是与 Felix Thimm 合作项目的一部分，致力于通过实现 Pardon 的维度 4 程序来证明 Calabi-Yau 4-流形的 GW/PT-对应。
英文摘要
We build a cohesive topological theory of orientations on moduli stacks for non-compact complex-analytic Calabi-Yau $4$-folds by extending and generalising the work of Joyce and Upmeier, and the work of Bojko. As a result, we get, in particular, canonical family orientations for all moduli spaces of Pandharipande-Thomas pairs. Our proofs use the algebraic topology of mapping spaces representing $KU$- and $KO$- theory, as well as some properties of the Lie groups $E_8$ and, surprisingly, $\operatorname{HSpin}(16)$. This is part of a joint project with Felix Thimm dedicated to the proof of the $GW/PT$-correspondence for Calabi-Yau $4$-folds by implementing Pardon's programme in dimension $4$.
Commentsv. 1: any comments are most welcome!
