Legendrian Fronts for Affine Varieties

Abstract

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 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 addition, we prove that the Koras--Russell cubic is Stein deformation equivalent to affine complex 3-space and verify the affine parts of the algebraic mirrors of two Weinstein 4-manifolds.

arXiv comment60 pages, lots of figures!

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Cited by in corpus (22)

• Duality between Lagrangian and Legendrian invariants
• Legendrian Weaves: N-graph Calculus, Flag Moduli and Applications
• Homological mirror symmetry for log Calabi-Yau surfaces
• Simplifying Weinstein Morse functions
• Bypass attachments in higher-dimensional contact topology
• Getting a handle on contact manifolds
• Geometric and algebraic presentations of Weinstein domains
• Chekanov-Eliashberg dg-algebras for singular Legendrians
• An introduction to Weinstein handlebodies for complements of smoothed toric divisors
• Arboreal singularities from Lefschetz fibrations
• Orientations of Morse flow trees in Legendrian contact homology
• Koszul duality via suspending Lefschetz fibrations
• A Lagrangian filling for every cluster seed
• Weinstein handlebodies for complements of smoothed toric divisors
• Exact Calabi-Yau categories and odd-dimensional Lagrangian spheres
• To compute orientations of Morse flow trees in Legendrian contact homology
• Exotic families of symplectic manifolds with Milnor fibers of $ADE$-type
• Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings
• Weinstein presentations for high-dimensional antisurgery
• Symplectomorphisms of some Weinstein 4-manifolds
• Homological invariants of codimension 2 contact submanifolds
• Arboreal singularities and loose Legendrians I