Essential Laminations

基本叠片

• 批准号: 9971333
• 负责人: Rachel Roberts
• 金额: $ 7.54万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-15 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9971333&HistoricalAwards=false
• 关键词: Essential; Laminations

Proposal: DMS-9971333PI: Rachel RobertsAbstract: Professor Roberts proposes to study essential laminations in 3-manifolds. There aretwo main directions of investigation. The firstinvolves working at better understanding nonexistence of essential laminations, boththrough understanding group actions onorder trees (in collaboration with Professor M. Stein) and, moredirectly, throughthe use of``standard forms''. The secondinvolves searching for constructions which give new information about exceptionalsurgeries on knots and links.In this research, Professor Roberts investigatesquestions concerning the structure of 3-manifolds,which are spaces formed by piecingtogether blocks of 3-dimensional space accordingto certain rules. Globally, the spaces obtainedare usually quite complex and model manyinteresting phenomena. Our spatial universe,for example, is a 3-manifold which it is crucial to understand. The studyof 3-manifolds is also important in thestudy of the knotting and linking of stringsin 3-dimensional space, which in turn isimportant in the study of the structure of DNA.

提案：DMS-9971333PI：Rachel Roberts 摘要：Roberts 教授建议研究 3 流形中的基本叠片。主要有两个研究方向。第一个涉及更好地理解基本分层的不存在，通过理解顺序树上的群体行为（与 M. Stein 教授合作），更直接地通过使用“标准形式”。第二个涉及寻找能够提供关于结和链接的特殊手术的新信息的结构。在这项研究中，罗伯茨教授研究了有关3维流形结构的问题，3流形是根据一定规则将3维空间块拼接在一起形成的空间。在全球范围内，获得的空间通常非常复杂，并且模拟了许多有趣的现象。例如，我们的空间宇宙是一个三流形，理解这一点至关重要。 3-流形的研究对于3维空间中弦的打结和连接也很重要，这反过来对于DNA结构的研究也很重要。