Abstract: The symmetric union is a construction introduced by Kinoshita and Terasaka in 1957 and generalized by Lamm in 2000. This construction is a generalization of the connected sum of a knot with its mirror image which producesplenty examples of ribbon knots. It is still an open question whether every ribbon knot admits a symmetric union presentation. In these talks we will discuss this question and the relationship between the knot type of a symmetric union and of its partial knot. We will also discuss some finiteness result wih respect to the partial knots. This is a joint work with Teruaki Kitano (Soka University) and Yuta Nozaki (Yokohama National University).
