Simple spines of homotopy 2-spheres are unique

Orson, P. and Powell, M. (2024) Simple spines of homotopy 2-spheres are unique. Proceedings of the London Mathematical Society, 128(2), e12583. (doi: 10.1112/plms.12583)

Abstract

A locally flatly embedded 2-sphere in a compact 4-manifold X is called a spine if the inclusion map is a homotopy equivalence. A spine is called simple if the complement of the 2-sphere has abelian fundamental group. We prove that if two simple spines represent the same generator of H2(X) then they are ambiently isotopic. In particular, the theorem applies to simple shake-slicing 2-spheres in knot traces.

• Item Type: Articles
• Additional Information: Funding information: SNSF, Grant/Award Number: 181199;EPSRC, Grant/Award Numbers: EP/T028335/2, EP/V04821X/2
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Powell, Professor Mark
• Authors: Orson, P., and Powell, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the London Mathematical Society
• Publisher: Wiley for the London Mathematical Society
• ISSN: 0024-6115
• ISSN (Online): 1460-244X
• Copyright Holders: Copyright: © 2024 The Authors
• First Published: First published in Proceedings of the London Mathematical Society 128(2): e12583
• Publisher Policy: Reproduced under a Creative Commons licence

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Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
320909		Classifying 4-manifolds	Mark Powell	Engineering and Physical Sciences Research Council (EPSRC)	EP/T028335/2	M&S - Mathematics
320615		Symmetries of 4-manifolds	Mark Powell	Engineering and Physical Sciences Research Council (EPSRC)	EP/V04821X/2	M&S - Mathematics