Sala Riunioni (Dip. Matematica).
slice knots (bounding smooth disks in the 4-space) play an important role in knot theory. They can be studied through examining the branched cover of the three-sphere along the given knot. In the lecture we describe two results around these questions, one involving many branched covers, the other concentrating on double branched covers, together with the covering involution, and how these data can be used in a Heegaard Floer theoretic construction.