弦结构和规范3-形式
String structures and canonical 3-forms
摘要：
利用基本的同伦构造，我们证明了自旋丛上弦结构的同构类自然地由丛的全空间上的某个3度上同调类给出，我们称之为弦类。使用霍奇同构，然后，我们表明，谐波代表的字符串类产生一个典型的3-形式的底空间，完善相关的微分字符。我们明确地计算这3-形式的齐次度量的3-球，我们讨论了如何上同调理论tmf可能编码的障碍，积极的里奇曲率度量。
英文摘要：
Using basic homotopy constructions, we show that isomorphism classes of string structures on spin bundles are naturally given by certain degree 3 cohomology classes, which we call string classes, on the total space of the bundle. Using a Hodge isomorphism, we then show that the harmonic representative of a string class gives rise to a canonical 3-form on the base space, refining the associated differential character. We explicitly calculate this 3-form for homogeneous metrics on 3-spheres, and we discuss how the cohomology theory tmf could potentially encode obstructions to positive Ricci curvature metrics.
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