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Surface slices and
homology spheres
Clayton McDonald |
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Geometry & Topology 30 (2026) 1611–1623
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Abstract |
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We develop the theory of the diagrammatics of surface cross sections to prove that there are an infinite number of homology 3-spheres smoothly embeddable in a homology 4-sphere but not in a homotopy 4-sphere. Our primary obstruction comes from work of Taubes. |
Keywords
embedding 3-manifolds in 4-manifolds
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Mathematical Subject Classification
Primary: 57K10, 57K41, 57K45, 57M10
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References |
Publication
Received: 28 August 2022
Revised: 10 November 2025
Accepted: 8 December 2025
Published: 18 July 2026
Proposed: Ciprian Manolescu
Seconded: Jianfeng Lin, András I Stipsicz
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Authors |
| Clayton McDonald | |
| HUN-REN Alfréd Rényi Institute of
Mathematics Budapest Hungary |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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