ﻻ يوجد ملخص باللغة العربية
Let $omega$ denote an area form on $S^2$. Consider the closed symplectic 4-manifold $M=(S^2times S^2, Aomega oplus a omega)$ with $0<a<A$. We show that there are families of displaceable Lagrangian tori $L_{0,x},, L_{1,x} subset M$, for $x in [0,1]$, such that the two-component link $L_{0,x} cup L_{1,x}$ is non-displaceable for each $x$.
In recent papers, summarized in survey [1], we construct a number of examples of non standard lagrangian tori on compact toric varieties and as well on certain non toric varieties which admit pseudotoric structures. Using this pseudotoric technique w
We study Dehn twists along Lagrangian submanifolds that are finite quotients of spheres. We decribe the induced auto-equivalences to the derived Fukaya category and explain its relation to twists along spherical functors.
We study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas from family Floer theory and tropical geometry to obtain both obstruc
In this paper we introduce the following new ingredients: (1) rework on part of the Lagrangian surgery theory; (2) constructions of Lagrangian cobordisms on product symplectic manifolds; (3) extending Biran-Cornea Lagrangian cobordism theory to the i
We consider a pair (H,I) where I is an involutive ideal of a Poisson algebra and H lies in I. We show that if I defines a 2n-gon singularity then, under arithmetical conditions on H, any deformation of H can integrated as a deformation of (H,I).