闭路空间上的字符串几何与自旋几何
String geometry vs. spin geometry on loop spaces
摘要：
基于Killingback的一个经典概念，我们引入了光滑流形的自由闭路空间上的自旋结构的不同版本，并进一步结合了环路之间的两个关系：薄同伦和环路融合.这篇文章的中心结果是闭路空间上的自旋结构和流形上的弦结构之间的等价性。等价性存在于两种情况下：一种是纯拓扑的，另一种是包括自旋连接和弦连接的几何的。我们的结果提供了一个一致的，函子的，一对一的字典之间的字符串几何和自旋几何闭路空间。
英文摘要：
We introduce various versions of spin structures on free loop spaces of smooth manifolds, based on a classical notion due to Killingback, and additionally coupled to two relations between loops: thin homotopies and loop fusion. The central result of this article is an equivalence between these enhanced versions of spin structures on the loop space and string structures on the manifold itself. The equivalence exists in two settings: in a purely topological one and a in geometrical one that includes spin connections and string connections. Our results provide a consistent, functorial, one-to-one dictionary between string geometry and spin geometry on loop spaces.
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