AI 中文总结
本文提出用等变单纯预层映射空间计算几何函子场论模空间的方法，并应用于一维定向黎曼函子场论。
AI 中文摘要
我们开发了计算几何函子场论模空间的工具，将其表示为等变单纯预层的映射空间。给定一个d维几何结构F，表示为d流形光滑族站点上的预层，我们定义其笛卡尔实现，即笛卡尔空间站点上的O(d)-等变单纯预层。我们利用笛卡尔实现将具有几何结构F的函子场论模空间呈现为O(d)-等变单纯预层之间的映射空间。在配套论文中，我们利用此结果计算了取值于任意光滑对称幺半无穷范畴的光滑一维定向黎曼函子场论的模空间。
英文摘要
We develop tools to compute moduli spaces of geometric functorial field theories as mapping spaces of equivariant simplicial presheaves. Given a d-dimensional geometric structure F, presented as a presheaf on the site of smooth families of d-manifolds, we define its Cartesian realization, which is an O(d)-equivariant simplicial presheaf on the site of Cartesian spaces. We use Cartesian realizations to present the moduli space of functorial field theories with geometric structure F as a mapping space between O(d)-equivariant simplicial presheaves. In a companion paper, we use this result to compute the moduli space of smooth one-dimensional oriented Riemannian functorial field theories valued in an arbitrary smooth symmetric monoidal infinity-category.
Comments44 pages. Comments and questions are welcome
