# Crossing with the circle in Dijkgraaf–Witten theory and applications to topological phases of matter

@article{Bullivant2021CrossingWT, title={Crossing with the circle in Dijkgraaf–Witten theory and applications to topological phases of matter}, author={Alex Bullivant and Clement Delcamp}, journal={Journal of Mathematical Physics}, year={2021} }

Given a fully extended topological quantum field theory, the “crossing with the circle” conditions establish that the dimension, or categorification thereof, of the quantum invariant assigned to a closed k-manifold Σ is equivalent to that assigned to the ( k + 1)-manifold [Formula: see text]. We compute in this paper these conditions for the 4-3-2-1 Dijkgraaf–Witten theory. In the context of the lattice Hamiltonian realization of the theory, the quantum invariants assigned to the circle and the…

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