论文标题
主$ \ infty $捆绑和平滑的字符串组型号
Principal $\infty$-Bundles and Smooth String Group Models
论文作者
论文摘要
我们在$ \ infty $ - 平滑空间的类别中提供了弦模型模型的一般，同质理论的定义，并为字符串组提供了新的平滑模型。在这里，光滑的空间是笛卡尔空间类别上$ \ infty $ groupoids的预毛。我们的定义和平滑字符串组模型的构建的关键是单数复合函数的版本，该版本将其分配给平滑空间一个基础的普通空间。我们提供了$ \ infty $ -topoi的主要$ \ infty $捆绑包和集团扩展的新特征，并在尼古拉斯，施雷伯和史蒂文森的工作基础上建立。这些见解使我们能够将字符串扩展的定义从$ \ infty $ - 空间的$ \ infty $类别转移到平滑空间的$ \ infty $ - 类别。最后，我们将出现的平滑高级群体扩展视为对Gerbes上的模棱两可结构存在的障碍。我们表明，这些扩展为与Müller和Szabo的联合工作中的猜想产生了新的平滑模型。
We provide a general, homotopy-theoretic definition of string group models within an $\infty$-category of smooth spaces, and we present new smooth models for the string group. Here, a smooth space is a presheaf of $\infty$-groupoids on the category of cartesian spaces. The key to our definition and construction of smooth string group models is a version of the singular complex functor, which assigns to a smooth space an underlying ordinary space. We provide new characterisations of principal $\infty$-bundles and group extensions in $\infty$-topoi, building on work of Nikolaus, Schreiber, and Stevenson. These insights allow us to transfer the definition of string group extensions from the $\infty$-category of spaces to the $\infty$-category of smooth spaces. Finally, we consider smooth higher-categorical group extensions that arise as obstructions to the existence of equivariant structures on gerbes. We show that these extensions give rise to new smooth models for the string group, as recently conjectured in joint work with Müller and Szabo.
