Embedded surfaces with infinite cyclic knot group

Conway, Anthony¹ ; Powell, Mark²

¹ Department of Mathematics, Massachussetts Institute of Technology, Cambridge, MA, United States
² School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom

Geometry & topology, Tome 27 (2023) no. 2, pp. 739-821.

Résumé

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.

Détail

DOI : 10.2140/gt.2023.27.739

Keywords: knotted surfaces, 4–manifolds, topological surgery

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