Paolo Aceto (Université de Lille) : Some problems in low-dimensional topology

The purpose of this talk is to provide a brief introduction to some key questions in low-dimensional topology. More specifically, we will focus on questions which are related to the interplay between the dimensions three and four. We will look at knots in the 3-sphere and surfaces bounded by such knots in the 4-ball. This leads to the notion of knot concordance and of the concordance group. Closely related is the notion of homology cobordisms of 3-manifolds and its corresponding group. We will describe these objects, comment on some fundamental open questions and closely examine a few key examples.