Upper bounds for the Lagrangian cobordism relation on Legendrian links
arXiv:2105.02390 · doi:10.2140/agt.2024.24.4237
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 tight 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.
21 pages, 19 figures