Embedded surfaces with infinite cyclic knot group

Conway, Anthony; Powell, Mark

doi:10.2140/gt.2023.27.739

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Embedded surfaces with infinite cyclic knot group

Anthony Conway and Mark Powell

Geometry & Topology 27 (2023) 739–821

DOI: 10.2140/gt.2023.27.739

Abstract

We study locally flat, compact, oriented surfaces in $4$ –manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$ , to be related by an ambient homeomorphism, and further criteria that imply they are ambiently isotopic. Along the way, we provide a classification of a subset of the topological $4$ –manifolds with infinite cyclic fundamental group, and we apply our results to rim surgery.

Keywords

knotted surfaces, 4–manifolds, topological surgery

Mathematical Subject Classification

Primary: 57K40, 57N35

References

Publication

Received: 11 November 2020

Revised: 5 August 2021

Accepted: 3 November 2021

Published: 16 May 2023

Proposed: András I Stipsicz

Seconded: Ciprian Manolescu, David Gabai

Authors

Anthony Conway
Department of Mathematics Massachussetts Institute of Technology Cambridge, MA United States

Mark Powell
School of Mathematics and Statistics University of Glasgow Glasgow United Kingdom

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Volume 27, issue 2 (2023)