论文标题
积分检测学位3弦弦乐类
Integrals detecting degree 3 string cobordism classes
论文作者
论文摘要
第三个字符串Bordism组$ \ MATHRM {BORD} _3^{\ MATHRM {String}} $是$ \ Mathbb {z}/24 \ Mathbb {z} $。 Bunke-Naumann和Redden使用Waldorf的几何弦结构的概念，表现出涉及Chern-Weil形式的积分公式，代表了第一个Pontryagin类的代表，以及几何的几何弦结构的规范3型，它们意识到了同构的同性形态，以意识到同性形态$ \ Mathrm {Bord} _ {bord} _ {bort} \ mathbb {z}/24 \ mathbb {z} $。当人们认为某些天然$ \ mathrm {u}（1）$ - 值和$ \ mathbb {r} $ - 估价的3D TQFT与与串联的串联堆叠相关联，分别与几何结构相关联时，我们将展示这些公式如何自然出现。
The third string bordism group $\mathrm{Bord}_3^{\mathrm{String}}$ is known to be $\mathbb{Z}/24\mathbb{Z}$. Using Waldorf's notion of a geometric string structure on a manifold, Bunke--Naumann and Redden have exhibited integral formulas involving the Chern-Weil form representative of the first Pontryagin class and the canonical 3-form of a geometric string structure that realize the isomorphism $\mathrm{Bord}_3^{\mathrm{String}} \to \mathbb{Z}/24\mathbb{Z}$. We will show how these formulas naturally emerge when one considers certain natural $\mathrm{U}(1)$-valued and $\mathbb{R}$-valued 3d TQFT associated with the classifying stacks of Spin bundles with connection and of String bundles with geometric structure, respectively.
