FRG: Holomorphic Curves in Low Dimensional Topology

FRG：低维拓扑中的全纯曲线

• 批准号: 0244663
• 负责人: Yakov Eliashberg
• 金额: --
• 依托单位: American Institute of Mathematics
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0244663&HistoricalAwards=false
• 关键词: FRG; Holomorphic; Curves; Low; Dimensional

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.

DMS-0244663 Yakov Eliashberg，John Etnyre，Wu-Chung Hsiang，Michael Hutchings，Tomasz Mrowka，Peter Ozsvath，罗纳德Stern，Zoltan Szabo.这是数学科学重点研究组（FRG）的一个奖项，在征集下获得http://www.nsf.gov/pubs/2002/nsf02129/nsf02129.htmHolomorphic。该项目的目标是统一和协调研究领域的应用holomorphiccurves，以便：- 构造3维和4维流形的新的不变量;-发展证明流形之间的同构的新方法;- 一方面发现弦理论和辛几何之间的新关系，另一方面发现纽结理论和3-流形拓扑之间的新关系。这个项目的核心，嵌入式辛场理论，该项目的影响预计将比其发展低维拓扑的直接目标更广泛。我们希望新发展的方法能为我们理解拓扑学和理论物理学，特别是弦论之间的联系打开新的视野。该项目也应该具有重要的教育价值。特别是，在这个项目下，将开发一个论文主题数据库，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的主题来源。