Smooth surfaces with non-simply-connected complements

Abstract

We consider two constructions of surfaces in simply-connected 4 -manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author eGeom. Topol. 10 (2006) 27-56]. We also construct, for any group G satisfying some simple conditions, a simply connected symplectic manifold containing a symplectic surface whose complement has fundamental group G. In each case, we produce infinitely many smoothly inequivalent surfaces that are equivalent up to smooth s-cobordism and hence are topologically equivalent for good groups. © 2008 Mathematical Sciences Publishers.