arXiv subjects

Matthew Cellot

Publications and source records attributed to Matthew Cellot.

3 recordsLinked to original sources

arXiv2026

Graded-fusion 2-categories and quantum homotopy invariants of 4-manifolds

We introduce 3-group-graded extensions of fusion 2-categories, where 3-groups are modeled by 2-crossed modules. From this data, we derive a state-sum invariant of 4-manifolds equipped with a homotopy class of maps to a homotopy 3-type, or equivalently of flat 3-bundles over 4-manifolds. This invariant is nontrivial and generalizes the Douglas-Reutter invariant of 4-manifolds. To construct our invariant, we encode homotopy classes of maps to the classifying space of a 3-group $\sigma$ via $\sigma$-colorings of triangulations, and we generalize Pachner's theorem in this context.

math.GT↗

arXiv2025

Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology

These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of braided fusion categories (arXiv:2105.15167). They recount the mathematical arguments of the original paper from an expository angle, with background material covering the algebra and homotopy theory required to understand the statement and follow the proof. The notes are aimed at newcomers to the field of (braided) fusion 1- and 2-categories.

math.QA↗

arXiv2025

Higher path groupoids and the holonomy of formal power series connections

Building on ideas of Kohno, we develop a framework for the construction of higher holonomy functors via the transport of formal power series connections. Using these techniques, we obtain functors from the path groupoid, the path 2-groupoid, and the path 3-groupoid of a manifold. As an application, we construct a Gray functor from the path 3-groupoid of the configuration space of $m$ points in $\mathbb{R}^n$ for $n\geqslant 4$.

math.AT↗