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Orientation twisted homotopy field theories and twisted unoriented Dijkgraaf-Witten theory

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Young,  Matthew Bruce
Max Planck Institute for Mathematics, Max Planck Society;

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1810.04612.pdf
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Citation

Young, M. B. (2020). Orientation twisted homotopy field theories and twisted unoriented Dijkgraaf-Witten theory. Communications in Mathematical Physics, 374(3), 1645-1691. doi:10.1007/s00220-019-03478-5.

Cite as: http://hdl.handle.net/21.11116/0000-0005-F630-F
Abstract
Given a finite $\mathbb{Z}_2$-graded group $\hat{\mathsf{G}}$ with ungraded subgroup $\mathsf{G}$ and a twisted cocycle $\hat{\lambda} \in Z^n(B \hat{\mathsf{G}}; \mathsf{U}(1)_{\pi})$ which restricts to $\lambda \in Z^n(B \mathsf{G}; \mathsf{U}(1))$, we construct a lift of $\lambda$-twisted $\mathsf{G}$-Dijkgraaf--Witten theory to an unoriented topological quantum field theory. Our construction uses a new class of homotopy field theories, which we call orientation twisted. We also introduce an orientation twisted variant of the orbifold procedure, which produces an unoriented topological field theory from an orientation twisted $\mathsf{G}$-equivariant topological field theory.