Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Given a knot K in the 3-sphere and a smooth closed 4-manifold X, we say that K is slice in X if it bounds a smoothly embedded disc in $X - int(B^4)$. It is still an open question whether an exotic pair of closed 4-manifolds can be detected by the set of knots that are slice in them. In this talk I will discuss a generalisation of this concept from knots to links in the 3-sphere, and I will compare smooth sliceness with its topological counterpart. I will focus in particular on the construction of a 2-component link which is not smoothly slice in $S^2 x S^2$, and explain why the same argument does not apply in the topological category, in which the analogous question is still open.
This is joint work with Clayton McDonald.