Interactions of geometry and knot theory

几何与纽结理论的相互作用

• 批准号: FT160100232
• 负责人: Prof Jessica Purcell
• 金额: $ 63.43万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-06-30 至 2021-06-29
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT160100232
• 关键词: Interactions; geometry; knot; theory

This project aims to use recent breakthroughs in hyperbolic geometry and Kleinian groups to relate geometry to knots which are mathematical objects arising in microbiology, chemistry, physics, and mathematics. Knots are often studied via the space around them known as the knot complement. Knot complements decompose into geometric pieces, and the most common geometry is hyperbolic, which completely determines a knot. However, how to obtain information on the hyperbolic geometry of a knot from a classical description is unknown. This project will obtain information by uncovering results that would enable classification of even extremely complicated knots, and could affect mathematics and other fields.

该项目旨在利用双曲几何和Kleinian群的最新突破，将几何与微生物学，化学，物理学和数学中出现的数学对象结联系起来。纽结通常通过它们周围的空间来研究，称为纽结补集。纽结补集分解成几何片段，最常见的几何是双曲型，它完全决定了一个纽结。然而，如何从经典描述中获得有关纽结双曲几何的信息尚不清楚。该项目将通过揭示结果来获取信息，这些结果甚至可以对极其复杂的结进行分类，并可能影响数学和其他领域。