双曲类与TMF值四流形不变量中的消没律
The hyperbolic class and vanishing laws in a TMF-valued four-manifold invariant
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中文总结 AI 辅助
本文在谱Looijenga构造假设下计算TMF值四流形不变量的双曲值，得到Hopf元素η，并证明非零符号导致不变量消没，从而给出完整公式。
中文摘要 AI 辅助
在谱Looijenga构造的显式假设下，我们计算了Gukov、Krushkal、Meier和Pei在周期拓扑模形式中的零截面不变量的双曲平面值。该值为Hopf元素η，且邻接一个双曲平面等同于乘以该元素。早期工作在额外的配边对偶假设下获得了双曲值；此处我们直接从Looijenga限制映射推导，无需该假设。结合确定格上的湮灭与消没结果，这给出了光滑闭单连通自旋四流形上的完整值公式。特别地，非零符号迫使不变量消没，因此K3曲面的两个定向的值均为零。
英文摘要
Under explicit hypotheses on the spectral Looijenga construction, we compute the hyperbolic-plane value of the zero-section invariant of Gukov, Krushkal, Meier, and Pei in periodic topological modular forms. The value is the Hopf element eta, and adjoining a hyperbolic plane acts by multiplication by this element. Earlier work obtains the hyperbolic value under an additional cobordism-duality assumption; here we derive it directly from the Looijenga restriction maps without that assumption. Together with annihilation and vanishing results for definite lattices, this gives a complete value formula on smooth closed simply connected spin four-manifolds. In particular, nonzero signature forces the invariant to vanish, so both orientations of a K3 surface have value zero.
发表机构
- C. N. Yang Institute for Theoretical Physics, Stony Brook University（杨振宁理论物理研究所，石溪大学）
- Weinberg Institute, The University of Texas at Austin（温伯格研究所，德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。
