2017/12/21 by Sylvain Courte, Courte, Sylvain, Tobias Ekholm +1 · 1 citation
Mathematics · #57R17 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1712.07849
openalex publication_date 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An exact Lagrangian submanifold L in the symplectization of standard contact (2n-1)-space with Legendrian boundary Σ can be glued to itself along Σ. This gives a Legendrian embedding Λ(L,L) of the double of L into contact (2n+1)-space. We show that the Legendrian isotopy class of Λ(L,L) is determined by formal data: the manifold L together with a trivialization of its complexified tangent bundle. In particular, if L is a disk then Λ(L,L) is the Legendrian unknot.