Mathematical Sciences: Invariants for Knots and Links in 3-Manifolds

数学科学：3-流形中的结和链接的不变量

• 批准号: 9626140
• 负责人: Efstratia Kalfagianni
• 金额: $ 7.18万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-15 至 1999-04-07
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626140&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Invariants; Knots; Links

9626140 Kalfagianni This project lies in the general area of low-dimensional topology. The investigator will attempt to develop a theory of finite type invariants for knots and links in an arbitrary 3-manifold as a generalization of the Jones invariants. She will also study these invariants via geometric methods, and try to understand what types of knots they detect. Low-dimensional topology is mainly concerned with classifying spaces of dimensions three and four, where two spaces are treated as equivalent if one space can be deformed onto the other without tearing - this is known as a homeomorphic transformation. Such a classification, known as the topological classification, has been essentially carried out in dimensions other than three and four. It turns out that these two dimensions provide further technical difficulties, some of which are topics of much current interest as they interface with various ideas of modern physics.

9626140 Kalfagianni这个项目位于一般的低维拓扑领域。作为Jones不变量的推广，研究者将尝试发展任意3-流形中的纽结和链环的有限类型不变量理论。她还将通过几何方法研究这些不变量，并试图了解它们检测到哪些类型的结。低维拓扑主要涉及对三维和四维空间的分类，其中两个空间被视为等价的，如果一个空间可以变形到另一个空间而不被撕裂-这被称为同胚变换。这种被称为拓扑分类的分类基本上是在三维和四维之外的维度上进行的。事实证明，这两个维度提供了更多的技术困难，其中一些是当前非常感兴趣的话题，因为它们与现代物理学的各种思想相联系。