Galois symmetries of knot spaces

Abstract: 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.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

( video )

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Topological Quantum Field Theory Club (IST, Lisbon)

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