Title: On the sliceness of Whitehead doubles of torus knots
Speaker: Laura Wakelin
Abstract: A knot K in the 3-sphere is smoothly slice if it bounds a smoothly embedded disc in the 4-ball. This property is invariant under knot concordance and the relevant information is contained in an associated 4-manifold called the 0-trace of the knot, which motivates the following idea. Given any satellite knot K=P(T) with companion a (2,q)-torus knot T and pattern P of winding number 0 and wrapping number 2, I will present an explicit algorithm for constructing a knot K’’ which has the same 0-trace as a knot K’ that is concordant to K. In particular, this suggests a new strategy for approaching the longstanding conjecture that the negative Whitehead double of the right-handed trefoil knot is not smoothly slice. This is ongoing joint work with Charles Stine.
Some snacks will be provided before and after the talk.