Discrete transformation groups

离散变换组

• 批准号: 4000-2011
• 负责人: Hambleton, Ian
• 金额: $ 3.06万
• 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: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=520638
• 关键词: Discrete; transformation; groups

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.

几何学中的统一原则之一是，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。常见的对称性包括固体在空间中的旋转或反射，以及时空的洛伦兹变换。代数拓扑学研究连续运动的离散不变量和对称群，几何拓扑学研究的是微分流形或高维曲面的性质。几何学和拓扑学是一门蓬勃发展的研究学科，与数学、科学和工程的其他领域有着广泛的联系。