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Geometry-Topology Seminar

Thursday, November 3, 2011 - 5:15pm

Ana Lecuona

Penn State University

Location

Bryn Mawr College

Park 336

This talk is sponsored jointly with Temple, Bryn Mawr and Haverford, as part of their PATCH series.

The slice-ribbon conjecture states that a knot in the three sphere is the boundary of an embedded disc in the four ball if and only if it bounds a disc in the sphere which has only ribbon singularities. This conjecture was proposed by Fox in the early 70s. There doesn´t seem to be any conceptual reason for it to be true, but large families of knots (i.e. pretzel knots, two bridge knots) satisfy it. In this seminar we will prove that the conjecture remains valid for a large family of Montesinos knots. The proof is based on Donaldson´s diagonalization theorem for definite four manifolds.