arXiv subjects

Glen Lim

Publications and source records attributed to Glen Lim.

2 recordsLinked to original sources

arXiv2026

The half-signature extension of the 3D bordism bicategory and its representations

We construct the half-signature bordism bicategory $\mathbf{Bord}_{1,2,3}^\mathrm{sig/2}$ as a central extension of the 3-dimensional oriented bordism bicategory by $\mathbb{Z}$. This is an index $2$ subextension of the signature bordism bicategory. Following methods of Bartlett--Douglas--Schommer-Pries--Vicary, we construct a presentation of this bicategory and hence show that its linear representations are classified exactly by modular tensor categories.

math.GT↗

arXiv2026

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

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.

math.GT↗