Geometry and topology of symplectomorphism groups

辛同胚群的几何和拓扑

• 批准号: 371999-2009
• 负责人: Pinsonnault, Martin
• 金额: $ 1.68万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=483832
• 关键词: Geometry; topology; symplectomorphism; groups

Symplectic geometry provides the mathematical framework of classical mechanics in its Hamiltonian formulation. It also underlies modern approaches to quantum theories. During the past 20 years, the study of the interactions between classical and quantum systems, as well as the introduction of powerful geometrical and analytical techniques, has led to the discovery of new structures and phenomena peculiar to symplectic objects that have no counterparts in classical differential geometry and topology.

辛几何在其哈密顿公式中提供了经典力学的数学框架。它也是量子理论的现代方法的基础。在过去的20年中，经典和量子系统之间的相互作用的研究，以及强大的几何和分析技术的引入，导致了新的结构和辛对象特有的现象，没有对应的经典微分几何和拓扑学的发现。