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Upper bounds for the
Lagrangian cobordism relation on Legendrian links
Joshua M Sabloff, David Shea Vela-Vick and C-M Michael Wong |
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Algebraic & Geometric Topology 24 (2024) 4237–4263
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Abstract |
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Lagrangian cobordism induces a preorder on the set of Legendrian links in any contact –manifold. We show that any finite collection of null-homologous Legendrian links in a contact –manifold with a common rotation number has an upper bound with respect to the preorder. In particular, we construct an exact Lagrangian cobordism from each element of the collection to a common Legendrian link. This construction allows us to define a notion of minimal Lagrangian genus between any two null-homologous Legendrian links with a common rotation number. |
Keywords
Legendrian links, Lagrangian cobordisms
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Mathematical Subject Classification
Primary: 57K33
Secondary: 53D12, 57K10
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References |
Publication
Received: 14 May 2021
Revised: 28 May 2023
Accepted: 2 July 2023
Published: 17 December 2024
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Authors |
| Joshua M Sabloff | |
| Department of Mathematics and
Statistics Haverford College Haverford, PA United States |
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| https://jsabloff.sites.haverford.edu | |
| David Shea Vela-Vick | |
| Department of Mathematics Louisiana State University Baton Rouge, LA United States |
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| https://www.math.lsu.edu/~shea | |
| C-M Michael Wong | |
| Department of Mathematics and
Statistics University of Ottowa Ottowa, ON Canada |
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| https://mysite.science.uottawa.ca/cwong | |
| © 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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