2025/07/22 by James Hughes, Jun Ma, Hughes, James +1
Engineering · Mathematics · #53D10 #53D12 #57K10 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2507.16747
openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine when a Legendrian quasipositive 3-braid closure in standard contact ℝ3 admits an orientable or non-orientable exact Lagrangian filling. Our main result provides evidence for the orientable fillability conjecture of Hayden and Sabloff, showing that a 3-braid closure is orientably exact Lagrangian fillable if and only if it is quasipositive and the HOMFLY bound on its maximum Thurston-Bennequin number is sharp. Of possible independent interest, we construct explicit Legendrian representatives of quasipositive 3-braid closures with maximum Thurston-Bennequin number.