Mathematical Sciences: Topological Knot Theoretic Connections

数学科学：拓扑结理论联系

• 批准号: 9013738
• 负责人: Ruth Lawrence
• 金额: $ 4.11万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-12-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9013738&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topological; Knot; Theoretic

This research will focus on the Jones polynomial, an invariant in knot theory, and will use a new topological approach which replaces the algebraic and combinatorial techniques with a simpler geometric method. This research should give a deeper understanding of a problem posed in one field by investigating it in the language of other areas of connected knowledge. The study of the relations between this new geometric approach and those already established should lead to a better understanding of all of this theory and provide a unified approach. Knot theory is an area of research in topology and algebra that has a variety of applications to mathematical biology in the description of DNA and to theoretical physics; in particular, conformal field theory and statistical mechanics.

本研究将集中在琼斯多项式， 不变的纽结理论，并将使用一种新的拓扑方法 它取代了代数和组合技术， 更简单的几何方法 这项研究应该提供一个更深入的 通过调查了解某一领域的问题 其他相关知识领域的语言。 研究 这种新的几何方法和那些 已经建立的一个机制应有助于更好地了解所有 并提供了一个统一的方法。 纽结理论是拓扑学和代数学的一个研究领域 在数学生物学中有很多应用， DNA的描述和理论物理;特别是， 共形场论和统计力学。