Topology of Manifolds

流形拓扑

• 批准号: RGPIN-2014-05432
• 负责人: Nicas, Andrew
• 金额: $ 0.8万
• 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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=588417
• 关键词: Topology; Manifolds

Geometry is the study of shapes and spaces. The subject of topology is concerned with those features of geometry which remain unchanged after twisting, stretching or other deformations of a geometrical space. It includes such problems as coloring maps, distinguishing knots and classifying surfaces and their higher dimensional analogs. The goal of "large scale" geometry and topology is to understand those intrinsic features of an unbounded space which remain visible after measurements are taken at increasingly large scales. These ideas have many applications including the qualitative study of dynamical systems and of very large data sets and also mathematical problems arising in fundamental modern physics. The proposed research seeks to provide algebraic measures of subtle geometric and topological phenomena that could be relevant to these and other potential applications. The key concepts of a "boundary at infinity" and of "asymptotic dimension" will be explored.

几何是对形状和空间的研究。拓扑学的主题涉及几何空间在扭曲、拉伸或其他变形后保持不变的几何特征。它包括诸如着色图、区分结和分类表面及其高维类似物等问题。 “大规模”几何和拓扑的目标是了解无界空间的那些内在特征，这些特征在以越来越大的尺度进行测量后仍然可见。这些想法有许多应用，包括动力系统和非常大的数据集的定性研究，以及基础现代物理学中出现的数学问题。拟议的研究旨在提供可能与这些和其他潜在应用相关的微妙几何和拓扑现象的代数测量。将探讨“无穷远边界”和“渐近维数”的关键概念。