论文标题
弦乐器捆绑包
The stringor bundle
论文作者
论文摘要
我们建立了一个2-Hilbert捆绑包的框架，该框架可以严格定义“弦乐器束”，这是Stolz和Teichner在20年前未出版的预印象中预期的一个更高的差异几何对象。我们的框架包括相关的捆绑结构，使我们可以将2-Hilbert捆绑包与主要的2套捆和其结构2组的统一表示。我们证明，stolz-teichner stringor束在典型上是对2-Hilbert束的同构，从将我们的相关捆绑结构应用于歧管上的字符串结构以及我们在早期工作中发现的字符串2组的弦乐表示。这建立了与自旋歧管，旋转组的表示和纺纱束的完美类比。
We set up a framework of 2-Hilbert bundles, which allows to rigorously define the "stringor bundle", a higher differential geometric object anticipated by Stolz and Teichner in an unpublished preprint about 20 years ago. Our framework includes an associated bundle construction, allowing us to associate a 2-Hilbert bundle with a principal 2-bundle and a unitary representation of its structure 2-group. We prove that the Stolz-Teichner stringor bundle is canonically isomorphic to the 2-Hilbert bundle obtained from applying our associated bundle construction to a string structure on a manifold and the stringor representation of the string 2-group that we discovered in earlier work. This establishes a perfect analogy to spin manifolds, representations of the spin groups, and spinor bundles.
