2016/10/21 by Roger Casals, Emmy Murphy · 1 citation
Mathematics · #Affine transformation #Algebraic Geometry and Number Theory #Combinatorics #Fibration #Geometric and Algebraic Topology #Handlebody #Homotopy #Homotopy and Cohomology in Algebraic Topology #Isotopy #Mathematics #Pure mathematics #Rigidity (electromagnetism) #Symplectic geometry #Topology (electrical circuits) #math.AG #math.GT #math.SG #msc:53D05 #msc:53D10 #msc:53D12 #msc:53D37
paper · pdf · doi:10.1215/00127094-2018-0055
published as Duke Math. J. 168, no. 2 (2019), 225-323 · 60 pages, lots of figures!
arxiv created 2016/10/21 · openalex publication_date 2019/01/10 · arxiv updated 2019/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First, we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian handlebody. Then we present several new applications of this technique to symplectic topology. This includes the detection of flexibility and rigidity for several families of Weinstein manifolds and the existence of closed, exact Lagrangian submanifolds. In particular, we prove that the Koras–Russell cubic is Stein deformation-equivalent to C3, and we verify the affine parts of the algebraic mirrors of two Weinstein 4-folds.