Principal bundles in noncommutative differential geometry

非交换微分几何中的主丛

• 批准号: RGPIN-2017-04249
• 负责人: Cacic, Branimir
• 金额: $ 1.02万
• 依托单位: University of New Brunswick
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635289
• 关键词: Principal; bundles; noncommutative; differential; geometry

Noncommutative (NC) geometry is a generalisation of classical geometry that provides new mathematical tools for both mathematical problems and physical models by allowing for geometric spaces and spacetimes whose coordinates no longer necessarily commute. For example, NC geometry has been successfully applied both to solve major problems in foliation theory and to obtain a complete mathematical model of the integer quantum Hall effect in condensed matter physics. Typically, the basic strategy has been to compute quantities of interest as topological invariants of the relevant NC space. More recently, intriguing connections to number theory, theoretical physics, and the mathematics of signal processing have brought new significance to the differential geometry of NC spaces in its own right.

非对易(NC)几何是经典几何的推广，通过允许坐标不再交换的几何空间和时空，为数学问题和物理模型提供了新的数学工具。例如，NC几何已经成功地应用于解决面理理论中的主要问题，并获得了凝聚态物理中整数量子霍尔效应的完整数学模型。通常，基本策略一直是将感兴趣的量计算为相关NC空间的拓扑不变量。最近，与数论、理论物理和信号处理数学的有趣联系给NC空间的微分几何本身带来了新的意义。