Iterated spans and classical topological field theories
Iterated spans and classical topological field theories
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迭代跨度和经典拓扑场论
DOI：
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发表时间：
2014
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通讯作者：
R. Haugseng
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作者：
R. Haugseng
我们构建更高类别的迭代跨度，可能配备有更高类别局部系统形式的额外结构，并对它们的完全对偶对象进行分类。根据协同假设，这些产生了框架拓扑量子场论，这是弗里德-霍普金斯-卢里-泰勒曼的量子化程序中考虑的经典拓扑量子场论的框架版本。使用这种机制，我们还构造了辛派生代数栈和拉格朗日对应的 $$(infty ,1)$$(∞,1) 范畴，并表明其所有对象都是可对偶的。
We construct higher categories of iterated spans, possibly equipped with extra structure in the form of higher-categorical 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 topological quantum field theories considered in the quantization programme of Freed–Hopkins–Lurie–Teleman. Using this machinery, we also construct an $$(infty ,1)$$(∞,1)-category of symplectic derived algebraic stacks and Lagrangian correspondences and show that all its objects are dualizable.