Contact Floer Homology

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• 批准号: 0072658
• 负责人: Alexander Givental
• 金额: $ 18.83万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072658&HistoricalAwards=false
• 关键词: Contact; Floer; Homology

AbstractAward: DMS-0072658Principal Investigator: Alexandre B. GiventalIn Symplectic Topology, the properties in question are usuallyformalized in the language of Floer homology theory and Gromov-Witten invariants. The proposed project is to extend andintertwine these two formalisms in the context of Contact Topology.The generalization exhibits natural relationships with the stringtheory and, moreover, shows how the structures of classical andquantum field theory emerge form the stringy properties ofcontact Floer homology. The project is conceived as a joint workof the P.I. with Ya. Eliashberg (Stanford University) andH. Hofer (Courant Institute) and is a part of the larger project"Symplectic Field Theory" started by the latter two authorsseveral years ago.The project originates from Symplectic and Contact Topologylaunched in the beginning of the twentieth century by A. Hurwitzand H. Poincare and studying profound geometrical properties ofclassical mechanical systems. The mechanical notions of positionand momentum coordinates lead to the geometric notion of asymplectic structure, in which the Hamiltonian formulation ofmechanics becomes extremely natural. Contact structures are theodd-dimensional counterparts to symplectic structures. Inaddition to their appearances in the study of subspaces ofsymplectic manifolds, contact structures have been of particularinterest in dimension three, where geometric ideas areilluminating some difficult questions in topology

摘要奖：DMS-0072658主要研究者：Alexandre B。在辛拓扑中，所讨论的性质通常用Floer同调理论和Gromov-Witten不变量的语言形式化。我们的计划是在接触拓扑的背景下扩展和解释这两种形式主义，这种推广展示了与弦论的自然联系，并且展示了经典和量子场论的结构是如何从接触Floer同调的弦性质中出现的。该项目被认为是一个联合工作的PI。和雅。Eliashberg（斯坦福大学）和H.辛场论是由柯朗研究所（Courant Institute）提出的，是后两位作者几年前开始的更大项目“辛场论”的一部分。赫维赞德·H庞加莱和研究深刻的几何性质的经典力学系统。 位置和动量坐标的力学概念导致了辛结构的几何概念，在辛结构中，力学的哈密顿公式变得非常自然。 接触结构是辛结构的奇维对应物。 除了在辛流形的子空间研究中出现之外，接触结构在三维空间中也引起了人们的特别兴趣，在三维空间中，几何思想解释了拓扑学中的一些困难问题