Smooth surfaces with non-simply-connected complements

Abstract

We give 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. 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.

28 pages, 2 figures

References in corpus (2)

• Notes on Perelman's papers
• Topological triviality of smoothly knotted surfaces in 4-manifolds

Cited by in corpus (4)

• Embedded surfaces with infinite cyclic knot group
• Knotted surfaces in 4-manifolds and stabilizations
• Null-homologous exotic surfaces in 4-manifolds
• Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group