Geodesic
Upper bounds for the Lagrangian cobordism relation on Legendrian links
Sabloff, Joshua M1 ; Vela-Vick, David Shea2 ; Wong, C-M Michael3
1 Department of Mathematics and Statistics, Haverford College, Haverford, PA, United States
2 Department of Mathematics, Louisiana State University, Baton Rouge, LA, United States
3 Department of Mathematics and Statistics, University of Ottowa, Ottowa, ON, Canada
Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4237-4263

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Lagrangian cobordism induces a preorder on the set of Legendrian links in any contact 3–manifold. We show that any finite collection of null-homologous Legendrian links in a contact 3–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.

DOI : 10.2140/agt.2024.24.4237
Keywords: Legendrian links, Lagrangian cobordisms

Sabloff, Joshua M 1 ; Vela-Vick, David Shea 2 ; Wong, C-M Michael 3

1 Department of Mathematics and Statistics, Haverford College, Haverford, PA, United States
2 Department of Mathematics, Louisiana State University, Baton Rouge, LA, United States
3 Department of Mathematics and Statistics, University of Ottowa, Ottowa, ON, Canada 
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Sabloff, Joshua M; Vela-Vick, David Shea; Wong, C-M Michael. Upper bounds for the Lagrangian cobordism relation on Legendrian links. Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4237-4263. doi: 10.2140/agt.2024.24.4237

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