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Embedded surfaces with infinite cyclic knot group

Anthony Conway and Mark Powell

Geometry & Topology 27 (2023) 739–821
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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