Fortführung und Erweiterung des Projektes `Functoriality for Floer homology` und Erlernen der neuen Techniken entwickelt von H. Hofer

继续和扩展“Floer 同源函数性”项目并学习 H. Hofer 开发的新技术

• 批准号: 5454867
• 负责人: Professor Dr. Peter Albers
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2005
• 资助国家: 德国
• 起止时间: 2004-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5454867?language=en
• 关键词: Fortf; hrung; und; Erweiterung; des

The object of the proposed project is the theory of Floer homology in symplectic geometry. The principal problem to be analyzed is the question of functoriality for Floer homology with respect to symplectic immersions of positive codimension. This will lead to a large number of important new applications concerning e.g. symplectic invariants such as capacities and Gromov-Witten invariants and Lagrangian intersection results. We are using an approach based on a Lagrangian boundary value problem for Floer half-cylinders. The main problems are to extend this concept in broad generality which requires a careful analysis of holomorphic disks and to develop a suitable concept of obstruction classes and algebraic correction terms. We expect the new techniques currently developed by H. Hofer to be crucial in pursuing this project.

该项目的目的是在辛几何弗洛尔同调理论。要分析的主要问题是关于正余维辛浸入的Floer同调的函性问题。这将导致大量重要的新应用，例如辛不变量，如容量和Gromov-Witten不变量和拉格朗日相交结果。我们使用的方法的基础上的拉格朗日边值问题的Floer半圆柱体。主要的问题是扩展这一概念的广泛的一般性，这需要仔细分析全纯磁盘和发展一个合适的概念的障碍类和代数校正项。我们期待H.霍费尔对这个项目至关重要。