Geometric constructions in homotopy theory

同伦理论中的几何构造

• 批准号: 261400-2008
• 负责人: Stanley, Donald
• 金额: $ 1.24万
• 依托单位: University of Regina
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503650
• 关键词: Geometric; constructions; homotopy; theory

Our program involves applying methods from homotopy theory to goemetric problems. One way to do this is by studying the complement M\P of a polyhedron P in a manifold M. An example of a manifold would be the possible positions of a mechanical system such as the planets in the solar system. The polyhedron would then correspond to unallowed positions, such as two planets being in the same location. The complement M\P would then correspond to allowable positions. We use algebraic invariants to give us information about this complement. In the case of a mechanical system, these invariants can control the behaviour of the system.

我们的计划涉及将同伦理论的方法应用于几何问题。要做到这一点，一种方法是研究多面体P在流形M中的补M\P。流形的一个例子是机械系统的可能位置，如太阳系中的行星。然后，多面体将对应于不允许的位置，例如两个行星处于同一位置。补语M\P随后将对应于允许的位置。我们使用代数不变量来提供有关这个补码的信息。在机械系统的情况下，这些不变量可以控制系统的行为。