A light bulb theorem for disks

Abstract: I will present joint work with Peter Teichner in which we classify isotopy classes of embedded disks in a 4-manifold, for a particular kind of boundary conditions. The proof uses a trick of Cerf and involves a surprising application of homotopy groups of spaces of embeddings in codimension 3. Moreover, we recover light bulb theorems of Gabai and Schneiderman-Teichner by completely new techniques, which are even ”at the level of spaces”, so also give rise to some unexpected group structures.