Foundations of Symplectic Field Theory

辛场论基础

• 批准号: 157897074
• 负责人: Professor Dr. Kai Cieliebak
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/157897074?language=en
• 关键词: Foundations; Symplectic; Field; Theory

The goal of this project is to provide rigorous analytical foundations for symplectic field theory (SFT), a unified theory of holomorphic curves in symplectic manifolds formulated by Eliashberg, Givental and Hofer in 2000. This is based on a new approach to transversality for holomorphic curves which we developed in a previous project in the context of Gromov- Witten theory. The extension of this approach to more general SFT utilizes constructions of symplectic hypersurfaces and contact open books by Donaldson, Giroux and others. Our approach is more elementary than other ones (polyfolds or Kuranishi structures) and it naturally gives rise to finer invariants associated to symplectic resp. contact manifolds together with codimension two submanifolds.

这个项目的目标是为辛场论（SFT）提供严格的分析基础，辛场论是由Eliashberg，Givental和霍费尔在2000年提出的辛流形中全纯曲线的统一理论。这是基于一个新的方法，我们在以前的项目中开发的Gromov-维滕理论的背景下，全纯曲线的横截性。这种方法的扩展到更一般的SFT利用结构的辛超曲面和接触开放的书籍由唐纳森，吉鲁和其他人。我们的方法比其他方法（多重折叠或Kuranishi结构）更基本，它自然会产生更精细的辛不变量。切触流形和余维两个子流形。

项目成果

A note on the stationary Euler equations of hydrodynamics

关于流体力学平稳欧拉方程的注解

• DOI: 10.1017/etds.2015.50
• 发表时间: 2017
• 期刊: Ergodic Theory and Dynamical Systems
• 影响因子: 0.9
• 作者: K. Cieliebak;E. Volkov
• 通讯作者: E. Volkov

First steps in stable Hamiltonian topology

稳定哈密顿拓扑的第一步

• DOI: 10.4171/jems/505
• 发表时间: 2015
• 期刊: arXiv: Symplectic Geometry
• 作者: K. Cieliebak;E. Volkov
• 通讯作者: E. Volkov

Stable Hamiltonian structures in dimension 3 are supported by open books

开放书籍支​​持 3 维稳定哈密顿结构

• DOI: 10.1112/jtopol/jtt044
• 发表时间: 2014
• 期刊: Journal of Topology
• 影响因子: 1.1
• 作者: K. Cieliebak;E. Volkov
• 通讯作者: E. Volkov