Low-dimensional topology

Smooth four-manifolds – 4D topological manifolds with a smooth structure – are not well characterised. Funded by the European Research Council, the KnotSurf4d project aims to address this gap in the knowledge of higher dimensional manifolds by leveraging the genus function and its enhanced version that takes knots and their slice surfaces into account. This novel approach emphasising knots and their slice properties in various four-manifolds could ultimately provide a candidate for an invariant that is a smooth generalisation of the intersection form and that characterises smooth four-manifolds. The team will also study divisibility and torsion questions in the concordance group via knot Floer homology, as well as potential counterexamples for the famous Slice-Ribbon conjecture.