Crossed modules, homotopy 2-types, knotted surfaces and welded knots


Salle Duhem M3
Joao Faria Martins
Vendredi, 2 Avril, 2021 - 14:00 - 15:00

I will review the construction of invariants of knots, loop braids and knotted surfaces derived from finite crossed modules. I will also show a method to calculate the algebraic homotopy 2-type of the complement of a knotted surface $\Sigma$ embedded in the 4-sphere from a movie presentation of $\Sigma$. This will entail a categorified form of the Wirtinger relations for a knot group. Along the way I will also show applications to welded knots in terms of a biquandle related to the homotopy 2-type of the complement of the tube of a welded knots.

The last stages of this talk are part of the framework of the Leverhulme Trust research project grant:  RPG-2018-029:“Emergent Physics From Lattice Models of Higher Gauge Theory.