Links in homology spheres are homotopic to slice links – an application of the relative Whitney trick.

Christopher Davis (U. Wisconsin-Eau Claire)

Generalizing the notion of sliceness for links in S^3, a link in a homology sphere is called slice if it bounds a disjoint union of locally flat embedded disks in a contractible 4-manifold. It is trivial to see that any link in S^3 can be changed by a homotopy to a slice link, indeed any link is homotopic to the unlink. We prove that the same is true for links in homology spheres. Our argument passes through a novel geometric construction which we call the relative Whitney trick. If time permits we will explore an application of the relative Whitney trick to the existence of Whitney towers.

Slides for talk: