# Seminário de Teoria Quântica do Campo Topológica

## Próxima sessão

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

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.

Projecto FCT UIDB/04459/2020.

Para assistir aos seminários via Zoom são necessárias credenciais. Se ainda não está na nossa lista de correio, por favor subscreva os anúncios para recebê-las juntamente com a informação de novos seminários.

Organizadores correntes: José MourãoRoger PickenMarko Stošić

Mathseminars

Projectos FCT PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.