Topologically isotopic and smoothly inequivalent 2–spheres in simply connected 4–manifolds whose complement has a prescribed fundamental group.

We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2–spheres in simply connected 4–manifolds, which are topologically isotopic and whose complement has a prescribed fundamental group that satisfies some conditions. This class of groups include cyclic groups and the binary icosahedral group. These are the first known examples of such exotic embeddings of 2–spheres in 4–manifolds. Examples of locally flat embedded 2–spheres in a nonsmoothable 4–manifold whose complements are homotopy equivalent to smoothly embedded ones are also given.