Related papers: Flexible Lagrangians
We prove an existence h-principle for regular Lagrangians with Legendrian boundary in arbitrary Weinstein domains of dimension at least six; this extends a previous result of Eliashberg, Ganatra, and the author for Lagrangians in flexible…
We characterize regularity of Lagrangian submanifolds in Weinstein Lefschetz fibrations, establishing a conjecture of Giroux and Pardon. Our main result is the Weinstein analogue of a closed symplectic Lefschetz pencil result of Auroux,…
In this note, we first introduce a boundary problem for Lagrangian submanifolds, analogous to the problem for free boundary hypersurfaces and capillary hypersurfaces. Then we present several interesting examples of Lagrangian submanifolds…
We prove that the existence of regular Lagrangians can be given by existence of Weinstein Lefschetz fibrations with an hypothesis.
We give a combinatorial description of the Legendrian contact homology algebra associated to a Legendrian link in $S^1\times S^2$ or any connected sum $\#^k(S^1\times S^2)$, viewed as the contact boundary of the Weinstein manifold obtained…
We introduce a procedure for gluing Weinstein domains along Weinstein subdomains. By gluing along flexible subdomains, we show that any finite collection of high-dimensional Weinstein domains with the same topology are Weinstein subdomains…
We introduce the notion of affine Legendrian submanifolds in Sasakian manifolds and define a canonical volume called the $\phi$-volume as odd dimensional analogues of affine Lagrangian (totally real or purely real) geometry. Then we derive…
We obtain upper and lower bounds for the relative Gromov width of Lagrangian cobordisms between Legendrian submanifolds. Upper bounds arise from the existence of $J$-holomorphic disks with boundary on the Lagrangian cobordism that pass…
We study Weinstein 4-manifolds which admit Lagrangian skeleta given by attaching disks to a surface along a collection of simple closed curves. In terms of the curves describing one such skeleton, we describe surgeries that preserve the…
To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a $1$-dimensional measurement of the non-cylindrical portion of the…
We explain a connection between the algebraic and geometric properties of groups of contact transformations, open book decompositions, and flexible Legendrian embeddings. The main result is that, if a closed contact manifold $(V, \xi)$ has…
We construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities. This yields closed arboreal Lagrangian skeleta for Weinstein pairs and Weinstein 4-manifolds associated to max-tb Legendrian…
This article studies the deformation problem for compact special Lagrangians with boundary in a Calabi--Yau manifold, with each boundary component constrained along a given Lagrangian submanifold. The tangent vectors generating such…
Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…
We are interested in comparing properties of symplectic mapping class groups of symplectic manifolds of dimension four or higher with properties of classical mapping class groups of surfaces. For $n \geq 2$, consider a configuration of…
In any contact manifold of dimension $2n-1\geq 11$, we construct examples of closed legendrian submanifolds which are not diffeomorphic but whose lagrangian cylinders in the symplectization are hamiltonian isotopic.
We show that the presence of a plastikstufe induces a certain degree of flexibility in contact manifolds of dimension 2n+1>3. More precisely, we prove that every Legendrian knot whose complement contains a "nice" plastikstufe can be…
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on Legendrian knots. There are some known "elementary" building blocks for Lagrangian cobordisms that…
We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of R^{2n+1}. More precisely, we investigate the behavior of the Thurston-Bennequin number and (linearized) Legendrian contact…
Embedded Lagrangian cobordisms between Legendrian submanifolds are produced from isotopy, spinning, and handle attachment constructions that employ the technique of generating families. Moreover, any Legendrian with a generating family has…