Floer theory in gauge theory and symplectic geometry

规范论和辛几何中的弗洛尔理论

• 批准号: 0604890
• 负责人: Yi-Jen Lee
• 金额: $ 12.96万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604890&HistoricalAwards=false
• 关键词: Floer; theory; gauge; symplectic; geometry

DMS-0604890Yi-Jen LeeThe PI plans to continue pursuing her research in two directions: thefirst is a long program to relate the theories of Seiberg-Witten andOzsvath-Szabo. The second is a possible generalization of the PI'sprevious work on Floer-theoretic torsions to a Floer-theoretic analog of Chern-Simons perturbative invariants.This proposal showcases the recent fertile interactions betweenmathematics and high energy physics. Gauge-theoretic invariants,enumeratitve invariants of holomorphic curves, and Floer theory all have their origin in physics, yet have since yielded the most important recent results in the fields of low dimensional topology and symplectic geometry. The proposal deals with fascinating relations among these physics-inspired invariants, and their applications to topology."

PI计划继续在两个方向上进行她的研究：第一个是一个长期项目，将Seiberg-Witten和dozsvath - szabo的理论联系起来。第二是将PI先前关于花理论扭转的工作推广到chen - simons微扰不变量的花理论模拟。这个提议展示了最近数学和高能物理之间丰富的相互作用。规范论不变量、全纯曲线的枚举不变量和弗洛尔理论都有其物理学的起源，但在低维拓扑和辛几何领域中产生了最重要的最新成果。该提案涉及这些物理启发的不变量之间的迷人关系，以及它们在拓扑学中的应用。”