The Arf-Brown TQFT of Pin$^-$ Surfaces

@article{Debray2018TheAT,
  title={The Arf-Brown TQFT of Pin\$^-\$ Surfaces},
  author={Arun Debray and Sam Gunningham},
  journal={arXiv: Mathematical Physics},
  year={2018}
}
The Arf-Brown invariant $\mathit{AB}(\Sigma)$ is an 8th root of unity associated to a surface $\Sigma$ equipped with a pin$^-$ structure. In this note we investigate a certain fully extended, invertible, topological quantum field theory (TQFT) whose partition function is the Arf-Brown invariant. Our motivation comes from the recent work of Freed-Hopkins on the classification of topological phases, of which the Arf-Brown TQFT provides a nice example of the general theory; physically, it can be… 
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