## – Europe/Lisbon

— Online

Pedro Boavida de Brito, Instituto Superior Técnico and CAMGSD

Galois symmetries of knot spaces

I’ll describe how the absolute Galois group of the rationals acts on a space which is closely related to the space of all knots. The path components of this space form a finitely generated abelian group which is, conjecturally, a universal receptacle for integral finite-type knot invariants. The added Galois symmetry allows us to extract new information about its homotopy and homology beyond characteristic zero. I will then discuss some work in progress concerning higher-dimensional variants.

This is joint work with Geoffroy Horel.

### Additional file

Projecto FCT `UIDB/04459/2020`.