FRG: Holomorphic Curves in Low Dimensional Topology

yakov Eliashberg, John Etnyre, Wu-Chung Hsiang, Michael Hutchings, Tomasz Mrowka, Peter Ozsvath, Ronald Stern, Zoltan Szabo。这是数学科学部重点研究小组（FRG）在征集中获得的奖项http://www.nsf.gov/pubs/2002/nsf02129/nsf02129.htmHolomorphic曲线最近在低维拓扑中出现了一个强大的工具。本项目的目标是联合和协调全纯曲线应用领域的研究，以便：-构造3维和4维流形的新不变量；-发展证明流形间差分同构的新方法；-一方面发现弦理论和辛几何之间的新关系，另一方面发现结理论和3流形拓扑之间的新关系。该项目的核心，嵌入式辛场理论，有望为低维拓扑中许多看似不同的问题提供统一的方法。该项目的影响预计将比其发展低维拓扑的直接目标广泛得多。新开发的方法有望为我们理解拓扑学和理论物理学之间的联系，特别是弦理论之间的联系开辟新的视野。该项目还应具有重要的教育价值。特别是，在该项目下，将建立一个论文主题数据库，这是一个积极管理和支持的问题列表，将作为高级项目人员的研究生博士论文主题的来源。

DMS-0244663Yakov Eliashberg, John Etnyre, Wu-Chung Hsiang, Michael Hutchings, Tomasz Mrowka, Peter Ozsvath, Ronald Stern, Zoltan Szabo.This is a Division of Mathematical Sciences Focused Research Group (FRG) award made under solicitation http://www.nsf.gov/pubs/2002/nsf02129/nsf02129.htmHolomorphic curves recently have emergedas a powerful tool in low-dimensional topology.The goal of this project is to unite and coordinateresearch in the area of applications of holomorphiccurves in order to: - construct new invariants of manifolds of dimension 3 and 4;- develop new methods for proving diffeomorphism between the manifolds;- find new relations between string theory and symplectic geometry on the one side, and knot theory and topology of 3-manifolds on the other.The core of this project, Embedded SymplecticField Theory, is expected to provide a unified approachto many seemingly different problems in low-dimensionaltopologyThe impact of this project is expected to be much broaderthan its immediate goal of developing low-dimensionaltopology. There is a hope that the newly developed methodsopen new horizons in our understanding of linksbetween Topology and Theoretical Physics, and in particularString Theory. The project should also have a significanteducational value. In particular, under this project therewill be developed a Dissertation Subject Database,an actively managed and supported list of problems which willserve as a source of topics of PhD dissertation for graduatestudents of the senior project personnel.