Double Point Surgery and Configurations of Surfaces in 4-manifolds

We introduce a new operation, double point surgery, on a configuration of surfaces in a 4-manifold, and use it to construct configurations that are smoothly knotted, without changing the topological type or the smooth embedding type of the individual components of the configuration. Taking branched covers, we produce smoothly exotic actions of $Z_m \oplus Z_n$ on simply connected 4-manifolds with complicated fixed-point sets.