Geometry and Topology Seminar

We say that a 2-component codimension-2 link in S^n is split when its components lie in disjoint balls. I'll talk about recent work proving that split 2-component links in S^4 can admit distinct non-isotopic splitting spheres, which contradicts classical intuition since any two splitting spheres in the complement of a 2-component split link in S^3 are isotopic. Specifically, I'll talk about this classical motivation, some recent work on interesting embeddings of 2- and 3-manifolds in S^4, and some of my favorite classical theorems in 4-dimensional topology. This is joint work with Mark Hughes and Seungwon Kim.