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.

几何学中的一个统一原则是，复杂的系统，如行星和恒星的配置，通常可以通过它们的对称性来理解。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。离散不变量和连续运动的对称群在代数拓扑中进行研究，而几何拓扑则与微分流形或高维曲面的性质有关。几何和拓扑学是一个蓬勃发展的研究课题，与数学，科学和工程的其他领域有着广泛的联系。