All once-extended 3D TQFTs are Reshetikhin--Turaev theories

Glen Lim

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arXiv · 2608.26068

All once-extended 3D TQFTs are Reshetikhin--Turaev theories

Glen Lim

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Abstract

We present a direct geometric construction which extends the Reshetikhin--Turaev TQFT to circles. We prove that this agrees with the generators-and-relations approach of Bartlett--Douglas--Schommer-Pries--Vicary, thus providing an alternative to the Cerf-theoretic part of their classification of once-extended 3-dimensional TQFTs, and deduce as a result that all once-extended 3-dimensional TQFTs arise via our construction.

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Glen Lim. 2026-08-26. All once-extended 3D TQFTs are Reshetikhin--Turaev theories. https://arxiv.org/abs/2608.26068

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