论文标题
扩展场理论是本地的，并且具有分类的空间
Extended field theories are local and have classifying spaces
论文作者
论文摘要
我们表明，所有扩展的功能性领域理论均以拓扑结构和非人体学为局部。我们用几何数据（例如Riemannian指标或几何字符串结构）定义了边界式的平滑（无穷，d） - 类别，并证明它对目标s表示满足，这意味着局部属性。我们将此结果应用于与几何数据的功能性字段理论的一致性类别的分类空间，解决了Stolz和Teichner的猜想，内容涉及这种空间的存在。我们使用分类的空间构建来开发电力运营的几何理论，该理论是在Barthel，Berwick-Evans和Stapleton的最新工作之后。
We show that all extended functorial field theories, both topological and nontopological, are local. We define the smooth (infinity,d)-category of bordisms with geometric data, such as Riemannian metrics or geometric string structures, and prove that it satisfies codescent with respect to the target S, which implies the locality property. We apply this result to construct a classifying space for concordance classes of functorial field theories with geometric data, solving a conjecture of Stolz and Teichner about the existence of such a space. We use our classifying space construction to develop a geometric theory of power operations, following the recent work of Barthel, Berwick-Evans, and Stapleton.
