Group actions on manifolds and complexes

流形和复形上的群作用

• 批准号: RGPIN-2016-05111
• 负责人: Hambleton, Ian
• 金额: $ 2.91万
• 依托单位: McMaster University
• 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=635310
• 关键词: Group; actions; manifolds; complexes

One of the unifying principles in geometry is that complex systems, such as configurations of planets and stars can often be understood by means of their symmetries. Familiar symmetries include the rotations or reflections of solids in space and the Lorentz transformations of space-time. Discrete invariants and groups of symmetry of continuous motions are studied in algebraic topology, while geometric topology is concerned with the properties of differential manifolds, or higher-dimensional surfaces. Geometry and topology is a flourishing subject for research, with broad connections to other areas of mathematics, science and engineering.

几何学中的统一原理之一是，通常可以通过它们的对称性来理解复杂的系统，例如行星和恒星的配置。熟悉的对称性包括空间中固体的旋转或反射以及时空的洛伦兹变换。在代数拓扑中研究了离散的不变性和连续运动对称性组，而几何拓扑与差分流形或较高维表面的特性有关。几何和拓扑是研究的繁荣主题，与其他数学，科学和工程学领域具有广泛的联系。