Hee Jung Kim

It has been known from the work of Wall and Donaldson that there exist infinite families of homologous spheres in 4-manifolds that are topologically equivalent but not smoothly. In this talk, we discuss the examples of closed simply-connected smooth 4-manifolds for which every primitive ordinary homology class is represented by infinitely many smoothly distinct but topologically isotopic spheres that become smoothly isotopic after one stabilization. This is joint work with Dave Auckly, Paul Melvin, and Daniel Ruberman.