Ana Garcia Lecuona: On the slice-ribbon conjecture for Montesinos knots

Abstract: The slice-ribbon conjecture states that a knot in $S^3=partial B^4$ is the boundary of an embedded disc in $B^4$ if and only if it bounds a disc in $S^3$ which has only ribbon singularities. In this seminar we will prove the conjecture for a family of Montesinos knots. The proof is based on Donaldson's diagonalization theorem for definite four manifolds.