从 $3$-自旋到负 $r$-自旋：上同调场论与同调关系的极限
From $3$-spin to Negative $r$-spin: Limits of Cohomological Field Theories and Tautological Relations
AI总结：
本文证明负 r-自旋同调关系可由 Pixton 的 3-自旋关系推出，并由此推导其在同调 Chow 环中成立，特别地 r=2 时得到 Kazarian--Norbury K-关系在 Chow 环中成立。
AI中文摘要：
我们证明了 Chidambaram--Garcia-Failde--Giacchetto 的负 $r$-自旋同调关系是 Pixton 的 $3$-自旋关系的推论，对于所有 $r\ge2$ 成立，并由此推导出它们在 $\overline{\mathcal{M}}_{g,n}$ 的同调 Chow 环中成立。特别地，我们关于 $r=2$ 的结果意味着 Kazarian--Norbury $K$-关系在 Chow 环中成立。证明分为两个关键部分。第一部分表明由 Chiodo 类产生的同调关系蕴含负 $r$-自旋关系，这需要对 Givental--Teleman 图贡献的极限行为进行细致研究。在第二部分中，我们证明 Chiodo 关系是 Pixton 的 $3$-自旋关系的推论，这是 Janda 关于上同调场论同调关系工作的推广的一个应用。
英文摘要：
We prove that the negative $r$-spin tautological relations of Chidambaram--Garcia-Failde--Giacchetto are a consequence of Pixton's $3$-spin relations, for every $r\ge2$, and deduce that they hold in the tautological Chow ring of $\overline{\mathcal{M}}_{g,n}$. In particular, our result for $r=2$ implies that Kazarian--Norbury $K$-relations hold in Chow. The proof factors through two essential parts. The first part shows that the tautological relations arising from Chiodo's class imply the negative $r$-spin relations. This requires an intricate study of limiting behavior of the Givental--Teleman graph contributions. In the second part, we show that the Chiodo relations are a consequence of Pixton's $3$-spin relations as an application of a generalization of Janda's work on tautological relations from CohFTs.
