Title:  Splitting Spheres for S^2’s in S^4

Speaker: Alison Tatsuoka

Abstract: If K_1 \sqcup K_2 is a split link in S^4, a splitting sphere for K is an S^3 in S^4 such that K_1 lies in one connected component of S^4\S^3, and K_2 lies in the other. We show that there exist infinitely many pairwise non-isotopic splitting spheres for two unlinked, unknotted S^2’s in S^4. Along the way, we introduce barbell diffeomorphisms of 4-manifolds, as constructed by Budney-Gabai in their paper “Knotted 3-balls in S^4”.