Knot Theory in the 4th Dimension (I)

The aim of the following two talks will be to generalise the concept of knots in the 4th dimension. In particular, we will introduce the notion of slice knots and knot concordance.Slice knots were first defined in 1958 by Fox and Milnor, in the context of resolving singularities of surfaces in 4-manifolds.Nevertheless, several other connections to questions that concern the 3- and 4-manifold topology have beendiscovered. Finally, the importance of slice knots arises from the fact that they enable us to make the set of all knots into a group.