Eclectic problems in topology, geometry and dynamics

拓扑、几何和动力学中的折衷问题

• 批准号: DP0342758
• 负责人: A/Prof Grant Cairns
• 金额: $ 9.27万
• 依托单位: La Trobe University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0342758
• 关键词: Eclectic; problems; topology; geometry; dynamics

This project aims to resolve a number of problems across several broad areas of pure mathematics. The problems all have a geometric or topological flavour, and some deal with dynamics in the qualitative sense. The problems share two common themes: they have group theoretic aspects and homological aspects. Specifically, the problems lie in the following areas: 1. finite dimensional Lie algebras and their cohomology, 2. low dimensional combinatorial geometry: graph drawings on surfaces, 3. topological dynamics of group actions, 4. differentiable group actions and foliation theory. The most significant aims are to resolve two well known conjectures: Halperin's toral rank conjecture and Conway's thrackle conjecture.

该项目旨在解决纯数学几个广泛领域的一些问题。这些问题都有几何或拓扑的味道，有些处理动态的定性意义上。这些问题有两个共同的主题：它们有群论方面和同调方面。具体而言，问题在于以下几个方面： 1.有限维李代数及其上同调， 2.低维组合几何：表面上的图形绘制， 3.群作用的拓扑动力学 4.可微群作用和叶理理论。 最重要的目标是解决两个著名的猜想：Halperin的toral rank猜想和Conway的thrackle猜想。