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Embedding surfaces in
$4$–manifolds
Daniel Kasprowski, Mark Powell, Arunima Ray and Peter Teichner |
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Geometry & Topology 28 (2024) 2399–2482
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Abstract |
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We prove a surface embedding theorem for –manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire–Milnor invariant for surfaces and we give a combinatorial formula for its computation. For this we introduce the notion of band characteristic surfaces. |
Keywords
embedding surfaces in 4–manifolds, Kervaire–Milnor
invariant
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Mathematical Subject Classification
Primary: 57K40, 57N35
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References |
Publication
Received: 4 October 2022
Revised: 28 February 2023
Accepted: 31 March 2023
Published: 24 August 2024
Proposed: Ciprian Manolescu
Seconded: Anna Wienhard, Mladen Bestvina
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Authors |
| Daniel Kasprowski | |
| School of Mathematical
Sciences University of Southampton Southampton United Kingdom |
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| Mark Powell | |
| School of Mathematics and
Statistics University of Glasgow Glasgow United Kingdom |
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| Arunima Ray | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| Peter Teichner | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| © 2024 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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