# The geometric cobordism hypothesis

@inproceedings{Grady2021TheGC, title={The geometric cobordism hypothesis}, author={Daniel Grady and Dmitri Pavlov}, year={2021} }

We prove a generalization of the cobordism hypothesis of Baez–Dolan and Hopkins–Lurie for bordisms with arbitrary geometric structures, such as Riemannian or Lorentzian metrics, complex and symplectic structures, smooth maps to a fixed target manifold, principal bundles with connections, or geometric string structures. Our methods rely on the locality property for fully extended functorial field theories established in arXiv:2011.01208, reducing the problem to the special case of geometrically…

## 5 Citations

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