Do you want to publish a course? Click here

Non-displaceable Lagrangian links in four-manifolds

148   0   0.0 ( 0 )
 Added by Cheuk Yu Mak
 Publication date 2019
  fields
and research's language is English




Ask ChatGPT about the research

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 $x$.



rate research

Read More

318 - Nikolai A. Tyurin 2019
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 we explain how non standard lagrangian tori of Chekanov type can be constructed and what is the topological difference between standard Liouville tori and the non standard ones. However we have not discussed the natural question about the periods of the constructed twist tori; in particular the monotonicity problem for the monotonic case was not studied there. In the paper we present several remarks on these questions, in particular we show for the monotonic case how to construct non standard lagrangian tori which satisify the monotonicity condition. First of all we study non standard tori which are Bohr - Sommerfeld with respect to the anticanonical class. This notion was introduced in [2], where one defines certain universal Maslov class for the ${rm BS}_{can}$ lagrangian submanifolds in compact simply connected monotonic symplectic manifolds. Then we show how monotonic non standard lagrangian tori of Chekanov type can be constructed. Furthemore we extend the consideration to pseudotoric setup and construct examples of monotonic lagrangian tori in non toric monotonic manifolds: complex 4 - dimensional quadric and full flag variety $F^3$.
149 - Cheuk Yu Mak , Weiwei Wu 2018
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 obstructions to and constructions of cobordisms; in particular, we give examples of symplectic tori in which the cobordism group has no non-trivial cobordism relations between pairwise distinct fibres, and ones in which the degree zero fibre cobordism group is a divisible group. The results are independent of but motivated by mirror symmetry, and a relation to rational equivalence of 0-cycles on the mirror rigid analytic space.
83 - Cheuk Yu Mak , Weiwei Wu 2015
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 immersed category. As a result, we manifest Seidels exact sequences (both the Lagrangian version and the symplectomorphism version), as well as Wehrheim-Woodwards family Dehn twist sequence (including the codimension-1 case missing in the literature) as consequences of our surgery/cobordism constructions. Moreover, we obtain an expression of the autoequivalence of Fukaya category induced by Dehn twists along Lagrangian $mathbb{RP}^n$, $mathbb{CP}^n$ and $mathbb{HP}^n$, which matches Huybrechts-Thomass mirror prediction of the $mathbb{CP}^n$ case modulo connecting maps. We also prove the split generation of any symplectomorphism by Dehn twists in $ADE$-type Milnor fibers.
269 - Mauricio Garay 2013
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).
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا