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arXiv · 2508.13759

A Boundary Characterization of Turaev-Viro TQFTs

Max-Niklas Steffen·Christoph Schweigert
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Abstract

We consider three-dimensional topological field theories on manifolds with boundary defects and identify explicit boundary locality conditions. We show that these conditions imply a state sum construction of the given TQFT. As a consistency check, we prove that Turaev-Viro state sum models obey the boundary locality conditions. Recent progress [Faria Martins J., Meusburger C., Adv. Math. 494 (2026), 110923, 102 pages, arXiv:2410.18049] in the description of defects in Dijkgraaf-Witten theories enables us to show that these theories likewise satisfy boundary locality. This directly implies that Dijkgraaf-Witten TQFTs with boundary defects admit a state sum description.

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Max-Niklas Steffen, Christoph Schweigert. 2025-08-19. A Boundary Characterization of Turaev-Viro TQFTs. https://doi.org/10.3842/sigma.2026.079

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