Knot concordance and 4-manifolds
There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will highlight some historical and recent connections between knot concordance (a weak notion of equivalence for knots) and the study of 4-manifolds, with a particular emphasis on applications of knot concordance to the construction and detection of small 4-manifolds which admit multiple smooth structures. I will also discuss a new method for using 4-manifolds to study knot concordance, and use it to show that the Conway knot is not slice.
Reception to follow at 4:30.