Knot traces and concordance
Knot traces and concordance
A conjecture of Akbulut and Kirby from 1978 states that the concordanceÌýclass of a knot is determined by its 0-surgery. In 2015, Yasui disprovedÌýthis conjecture by providing pairs of knots which have the sameÌý0-surgeries yet which can be distinguished in (smooth) concordance by anÌýinvariant associated to the four-dimensional traces of such a surgery.ÌýIn this talk, I will discuss joint work with Lisa Piccirillo in which weÌýconstruct many pairs of knots which have diffeomorphic 0-surgery tracesÌýyet some of which can be distinguished in smooth concordance by theÌýHeegaard Floer d-invariants of their double branched covers. If timeÌýpermits, I will also discuss the applicability of this work to theÌýexistence of interesting invertible satellite maps on the smoothÌýconcordance group.