Skein Kerler-Lyubashenko functors on 4-dimensional relative handlebodies

par Maksymilian Manko

mardi 8 déc. 2026, 11:15 → 12:15 Europe/Paris

Pellos

There has recently been interest in applying tools from the area of non-semisimple TQFTs to problems in 4-manifold topology. Two constructions standing out are Kerler-Lyubashenko (KL) functors due to Beliakova-De Renzi, defined for 4-dimensional 2-handlebodies (manifolds with boundary constructed with handles of index at most 2) up to Kirby moves of index at most 2, and skein (3+1)-TQFTs by Constantino-Geer-Haioun-Patureau-Mirand. In this talk I will explain how the skein technology can be used to reconstruct the KL functors and generalise them to all handle types, given appropriate algebraic input. As a corollary, I will show that, whenever 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 exotic pair detection and the conjecture of Gompf for 4-dimensional 2-handlebodies.