Paper
Embedded surfaces with infinite cyclic knot group
Authors
Anthony Conway, Mark Powell
Abstract
We study locally flat, compact, oriented surfaces in -manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus , to be related by an ambient homeomorphism, and further criteria that imply they are ambiently isotopic. Along the way, we prove that certain pairs of topological -manifolds with infinite cyclic fundamental group, homeomorphic boundaries, and equivalent equivariant intersection forms, are homeomorphic.