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Embedded surfaces with infinite cyclic knot group

Conway, A. and Powell, M. (2023) Embedded surfaces with infinite cyclic knot group. Geometry and Topology, 27(2), pp. 739-821. (doi: 10.2140/gt.2023.27.739)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Powell, Professor Mark
Authors: Conway, A., and Powell, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Geometry and Topology
Publisher:Mathematical Sciences Publishers
ISSN:1465-3060
ISSN (Online):1364-0380
Copyright Holders:Copyright © 2023 MSP (Mathematical Sciences Publishers).
First Published:First published in Geometry and Topology 27(2): 739-821
Publisher Policy:Reproduced under a Creative Commons licence
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