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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.
We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification $(M,mathbf
The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in Euclidean space. Our def
Let $X$ be a Weinstein manifold with ideal contact boundary $Y$. If $Lambdasubset Y$ is a link of Legendrian spheres in $Y$ then by attaching Weinstein handles to $X$ along $Lambda$ we get a Weinstein cobordism $X_{Lambda}$ with a collection of Lagra
We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that thi
We prove that the number of Reeb chords between a Legendrian submanifold and its contact Hamiltonian push-off is at least the sum of the $mathbb{Z}_2$-Betti numbers of the submanifold, provided that the contact isotopy is sufficiently small when comp