Exotic embeddings of $#6\Bbb R\roman{P}^2$ in the 4-sphere

Abstract

We present an infinite sequence of smooth embeddings of a connected sum of 6 projective planes in the 4-sphere, which are all ambient homeomorphic, but pairwise ambient non-diffeomorphic. The double covers of the 4-sphere ramified along these surfaces form a family of the exotic $\Bbb CP^2#5\bar{\Bbb CP^2}$ constructed recently by Park, Stipsicz and Szab\'o.