Eclectic problems in topology, geometry and dynamics

拓扑、几何和动力学中的折衷问题

• 批准号: ARC : DP0342758
• 负责人: Grant Cairns
• 金额: $ 13.3万
• 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://researchdata.edu.au/eclectic-problems-topology-geometry-dynamics/64771
• 关键词: Eclectic; problems; topology; geometry; dynamics

Eclectic problems in topology, geometry and 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:\r\n1. finite dimensional Lie algebras and their cohomology,\r\n2. low dimensional combinatorial geometry: graph drawings on surfaces,\r\n3. topological dynamics of group actions,\r\n4. differentiable group actions and foliation theory.\r\nThe most significant aims are to resolve two well known conjectures: Halperin's toral rank conjecture and Conway's thrackle conjecture.\r\n

拓扑、几何和动力学中的折衷问题。该项目旨在解决纯数学多个广泛领域的许多问题。这些问题都具有几何或拓扑性质，有些涉及定性意义上的动力学。这些问题有两个共同的主题：它们具有群论方面和同调方面。具体来说，问题存在于以下几个方面：\r\n1．有限维李代数及其上同调，\r\n2。低维组合几何：曲面上的图形绘制，\r\n3。群体行为的拓扑动力学，\r\n4。可微群作用和叶状理论。\r\n最重要的目标是解决两个众所周知的猜想：Halperin 的托拉秩猜想和 Conway 的 thrackle 猜想。\r\n