Splitting spheres in S^4

A 2-component link L is split if its components lie in disjoint balls. The boundary of either of these balls is called a splitting sphere for L. In the 3-sphere, 2-component split links have unique splitting spheres, meaning any two splitting spheres for L are isotopic in S^3-L. In this talk, we’ll discuss why this fails in dimension 4: many 2-component split links of surfaces in the 4-sphere do not have unique splitting spheres. (In fact, many unlinks have non-unique splitting spheres.)  This is joint work with Mark Hughes and Seungwon Kim.