Moment maps, moduli spaces and twisted K-theory

矩图、模空间和扭曲 K 理论

• 批准号: 203124-2006
• 负责人: Meinrenken, Eckhard
• 金额: $ 2.77万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=392690
• 关键词: Moment; maps; moduli; spaces; twisted

Summary of proposal for public release In his 1998 paper, the physicist Witten proposed that D-branes in string theory carry an ususual type of charge, known by mathematicians as `twisted K-theory'. Motivated by this remark, twisted K-theory has undergone rapid development, and was found to have many remarkable properties and applications. It is the aim of this proposal to study these and related topics in conjunction with symplectic geometry and the theory of moment maps. This research will have applications to the geometry of moduli spaces, which appear in many areas of mathematics (algebraic geometry, representation theory and knot theory) and physics (2-dimensional gauge theory, conformal field theory).

物理学家维滕在他1998年的论文中提出，弦论中的D膜带有一种常见的电荷，数学家称之为“扭曲K理论”。受此启发，扭曲K理论得到了迅速发展，并发现了许多显著的性质和应用。这是本建议的目的是研究这些和相关的主题与辛几何和理论的时刻地图。这项研究将应用于模空间的几何，这出现在数学（代数几何，表示论和纽结理论）和物理（2维规范理论，共形场论）的许多领域。