相关论文: Symplectic capacities of toric manifolds and relat…

Given $p\in [1,\infty]$, this article presents the novel basic volumetric estimates for the relative $p$-capacities with their applications to finding not only the sharp weak $(p,q)$-imbeddings but also the precise lower bounds of the…

Symplectic integrators with long-term preservation of integrals of motion are introduced for the guiding-center model of plasma particles in toroidal magnetic fields of general topology. An efficient transformation to canonical coordinates…

This is the second installment in a series of papers aimed at generalizing symplectic capacities and homologies. We study symmetric versions of symplectic capacities for real symplectic manifolds, and obtain corresponding results for them…

In this note, we study Seshadri constants and Gromov widths of toric surfaces via lattice widths of their moment polygons. We give the sharp lower bound of the ratio between the Gromov width of a symplectic toric $4$-fold and the lattice…

In this paper we present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S^1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a…

This paper studies the action of symplectic homeomorphisms on smooth submanifolds, with a main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic…

We consider aspherical manifolds with torsion-free virtually polycyclic fundamental groups, constructed by Baues. We prove that if those manifolds are cohomologically symplectic then they are symplectic. As a corollary we show that…

We introduce new invariants associated to collections of compact subsets of a symplectic manifold. They are defined through an elementary-looking variational problem involving Poisson brackets. The proof of the non-triviality of these…

We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Exemples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold.…

We define a cocycle on the group of symplectic diffeomorphisms of a symplectic manifold and investigate its properties. The main applications are concerned with symplectic actions of discrete groups. For example, we give an alternative…

A prequantization bundle is a negative circle bundle over a symplectic surface together with a contact form induced by a S1-invariant connection. Given a symplectically aspherical symplectic filling of a prequantization bundle satisfying…

The goal of this paper is to classify symplectic toric stratified spaces with isolated singularities. This extends a result of Burns, Guillemin, and Lerman which carries out this classification in the compact connected case. In making this…

We present a symplectic formulation of the $N =1$ four-dimensional type IIB scalar potential arising from a flux superpotential which has four S-dual pairs of fluxes demanded by the U-dual completion arguments. Our symplectic formulation…

This paper is concerned with the rational symplectic field theory in the Floer case. For this observe that in the general geometric setup for symplectic field theory the contact manifolds can be replaced by mapping tori of symplectic…

We study the four-dimensional (4D) scalar potential arising from a generalized type IIA flux superpotential including the (non-)geometric fluxes. First, we show that using a set of peculiar flux combinations, the 4D scalar potential can be…

We show that two orientable, four-dimensional folded symplectic toric manifolds are isomorphic provided that their orbit spaces have trivial degree-two integral cohomology and there exists a diffeomorphism of the orbit spaces (as manifolds…

Let $M$ be a symplectic manifold, equipped with a Hamiltonian action of a torus $T$. We give an explicit formula for the rational cohomology ring of the symplectic quotient $M//T$ in terms of the cohomology ring of $M$ and fixed point data.…

This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections.…

We introduce the cutting construction of possibly non-compact symplectic toric manifolds, in particular, toric symplectic cones that correspond to a weakly convex good cone. Since the symplectization of a toric contact manifold is a toric…

In this paper, we construct a sequence $(c_k)_{k\in\mathbb{N}}$ of symplectic capacities based on the Chiu-Tamarkin complex $C_{T,\ell}$, a $\mathbb{Z}/\ell$-equivariant invariant coming from the microlocal theory of sheaves. We compute…