Embedded surfaces with infinite cyclic knot group
Anthony Conway, Mark Powell
Abstract
We study locally flat, compact, oriented surfaces in 4-manifolds whose exteriors \nhave infinite cyclic fundamental group. We give algebraic topological criteria for two such \nsurfaces, with the same genus g, to be related by an ambient homeomorphism, and further \ncriteria that imply they are ambiently isotopic. Along the way, we provide a classification of \na subset of the topological 4-manifolds with infinite cyclic fundamental group, and we apply \nour results to rim surgery.
Topics & Concepts
MathematicsFundamental groupEquivariant mapHomeomorphism (graph theory)Knot (papermaking)Pure mathematicsIntersection (aeronautics)Group (periodic table)Surface (topology)GenusTopology (electrical circuits)CombinatoricsGeometryAerospace engineeringBiologyChemical engineeringChemistryBotanyOrganic chemistryEngineeringGeometric and Algebraic TopologyGeometric Analysis and Curvature FlowsMathematical Dynamics and Fractals