Geodesic arcs and surfaces for hyperbolic knots and 3-manifolds

双曲结和 3 流形的测地线弧和曲面

• 批准号: DP240102350
• 负责人: Prof Jessica Purcell
• 金额: $ 32万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-01-01 至 2026-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP240102350
• 关键词: Geodesic; arcs; surfaces; hyperbolic; knots

This project aims to use recent breakthroughs in mathematics to determine explicit geometric information on mathematical spaces, namely knot complements and 3-manifolds. These spaces arise in applications across science and engineering. They break into pieces that admit geometry, where hyperbolic geometry is the most common. This project expects to generate new knowledge around a number of open questions and conjectures on the hyperbolic geometry of knots and 3-manifolds. Expected outcomes include development of theory, and improved geometric tools. It will benefit the mathematical community through new insights and improved methods, and possibly lead to downstream applications in other scientific fields that rely on geometry.

该项目旨在利用数学上的最新突破来确定数学空间上的显式几何信息，即结补和3流形。这些空间出现在科学和工程领域的应用中。它们被分解成几何的部分，其中双曲几何是最常见的。该项目希望围绕结和3流形的双曲几何的一些开放问题和猜想产生新的知识。预期的结果包括理论的发展和几何工具的改进。它将通过新的见解和改进的方法使数学界受益，并可能导致依赖几何的其他科学领域的下游应用。