Embedded surfaces with infinite cyclic knot group

Conway, Anthony; Powell, Mark

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.

Citation

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

• Journal Article Type: Article
• Acceptance Date: Nov 3, 2021
• Online Publication Date: May 16, 2023
• Publication Date: 2023
• Deposit Date: Nov 15, 2021
• Publicly Available Date: Jun 21, 2023
• Journal: Geometry and Topology
• Print ISSN: 1465-3060
• Electronic ISSN: 1364-0380
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 2
• Pages: 739-821
• DOI: https://doi.org/10.2140/gt.2023.27.739
• Public URL: https://durham-repository.worktribe.com/output/1222164