迭代跨距与经典拓扑域论
Iterated spans and classical topological field theories
摘要：
我们构造高阶范畴的迭代跨度，可能配备额外的结构形式的“本地系统”，并分类其完全dualizable对象。通过协证假说，这些理论产生了框架拓扑量子场论，它是在Freed-Hopkins-Lurie-Teleman的量子化方案中考虑的“经典”TQFT的框架版本。利用这种机制，我们还构建了一个无穷大类的拉格朗日对应辛导出代数堆栈之间，并表明其所有的对象是完全对偶。
英文摘要：
We construct higher categories of iterated spans, possibly equipped with extra structure in the form of "local systems", and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum field theories, which are the framed versions of the "classical" TQFTs considered in the quantization programme of Freed-Hopkins-Lurie-Teleman. Using this machinery, we also construct an infinity-category of Lagrangian correspondences between symplectic derived algebraic stacks and show that all its objects are fully dualizable.
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