# Extended field theories are local and have classifying spaces

@inproceedings{Grady2020ExtendedFT, title={Extended field theories are local and have classifying spaces}, author={Daniel Grady and Dmitri Pavlov}, year={2020} }

We show that all extended functorial field theories, both topological and nontopological, are local. We define the smooth (∞, 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…

## 6 Citations

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