Document Type
Article
Publication Date
1-1-2024
Abstract
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.
Publication Source (Journal or Book title)
Algebraic and Geometric Topology
First Page
4237
Last Page
4263
Recommended Citation
Sabloff, J., Vela-Vick, D., & Wong, C. (2024). Upper bounds for the Lagrangian cobordism relation on Legendrian links. Algebraic and Geometric Topology, 24 (8), 4237-4263. https://doi.org/10.2140/agt.2024.24.4237