UBC Math Department Seminar: Sungkyung Kang

We say that a knot is slice if it bounds a smooth disk in 4-ball and ribbon if it bounds a ribbon disk in 3-sphere. Ribbon knots are always slice, while it is unknown whether the converse, also known as the slice-ribbon conjecture, is true. The simplest potential counterexample to the slice-ribbon conjecture is the (2,1)-cable of the figure-eight knot; Kawauchi asked whether it is slice in 1980. In this talk, I will present a proof that this knot is not slice, answering the 40-years-old question of Kawauchi. This is based on my work arXiv:2207.14187, joint with I. Dai, A. Mallick, J. Park, and M. Stoffregen.