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### Smoothly slice links in some 4-manifolds

**Geometry/Topology**

Speaker: | Marco Marengon, Alfréd Rényi Institute of Mathematics |

Related Webpage: | https://users.renyi.hu/~marengon/ |

Location: | 2112 MSB |

Start time: | Tue, Dec 12 2023, 4:10PM |

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.