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$3$–Manifolds without any
embedding in symplectic $4$–manifolds
Aliakbar Daemi, Tye Lidman and Mike Miller Eismeier |
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Geometry & Topology 28 (2024) 3357–3372
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Abstract |
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We show that there exist infinitely many closed –manifolds that do not embed in closed symplectic –manifolds, disproving a conjecture of Etnyre–Min–Mukherjee. To do this, we construct L–spaces that cannot bound positive- or negative-definite manifolds. The arguments use Heegaard Floer correction terms and instanton moduli spaces. |
Keywords
$3$–manifold, definite $4$–manifold, symplectic
$4$–manifolds, L–spaces, Chern–Simons invariant, instantons
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Mathematical Subject Classification
Primary: 57R57
Secondary: 57K43, 57R40
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References |
Publication
Received: 18 July 2022
Revised: 19 March 2023
Accepted: 19 May 2023
Published: 25 November 2024
Proposed: András I Stipsicz
Seconded: Dmitri Burago, Ciprian Manolescu
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Authors |
| Aliakbar Daemi | |
| Department of Mathematics and
Statistics Washington University St. Louis, MO United States |
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| Tye Lidman | |
| Department of Mathematics North Carolina State University Raleigh, NC United States |
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| Mike Miller Eismeier | |
| Department of Mathematics Columbia University New York, NY United States |
Department of Mathematics University of Vermont Burlington, VT United States |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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