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In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assuming such a smooth cancellation is possible. This technique is applied to show the existence h-principle for codimension-two contact embeddings with a prescribed contact structure.
In this paper we prove a convexity and fibre-connectedness theorem for proper maps constructed by Thimms trick on a connected Hamiltonian $G$-space $M$ that generate a Hamiltonian torus action on an open dense submanifold. Since these maps only gener
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
Sivek proves a van Kampen decomposition theorem for the combinatorial Legendrian contact algebra (also known as the Chekanov-Eliashberg algebra) of knots in standard contact $R^3$ . We prove an analogous result for the holomorphic curve version of th
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
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