Skein Kerler-Lyubashenko functors for relative 4-handlebodiesMPIM

by Maksymilian Manko Manko (Universität Zürich)

Monday Nov 2, 2026, 10:30 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Quantum topology seminar

There has recently been interest in applying tools from non-semisimple TQFTs to problems in 4-manifold topology. Two constructions stand out: the Kerler–Lyubashenko (KL) functors of Beliakova–De Renzi, defined for 4-dimensional 2-handlebodies
(manifolds with boundary built from handles of index at most 2) up to 2-deformations, and the skein (3+1)-TQFTs of Costantino–Geer–Haïoun–Patureau-Mirand. In this talk I will explain how the skein technology can be used to reconstruct a version of KL
functors and extend them to handles of all indices, given appropriate algebraic input. As a corollary, whenever both are defined, the invariants of 4-manifolds with boundary derived from the two constructions coincide. This is relevant for open problems in
4-dimensional topology, such as the Gompf’s conjecture for 4-dimensional 2-handlebodies.