Classical and quantum invariants of low-dimensional manifolds

低维流形的经典和量子不变量

• 批准号: DP190102363
• 负责人: A/Prof Craig Hodgson
• 金额: $ 21.06万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-06-20 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190102363
• 关键词: Classical; quantum; invariants; low; dimensional

This project aims to advance our understanding of knots and 3-dimensional spaces, which arise naturally in fields as diverse as physics, computer graphics, chemistry and biology. Recent ideas from quantum field theory link physics to topology in dimensions 3 and 4, leading to powerful invariants of knots and 3-dimensional manifolds that include the Jones polynomial and the 3D-index. This project aims to resolve key questions relating these quantum invariants to classical topology and geometry. The project will have a major impact in low-dimensional topology, and lead to deep and unexpected connections between mathematics and mathematical physics.

这个项目旨在促进我们对结和三维空间的理解，它们在物理、计算机图形学、化学和生物学等不同领域自然出现。量子场论的最新思想将物理学与3维和4维的拓扑联系起来，导致结点和三维流形的强大不变量，包括琼斯多项式和三维指数。本项目旨在解决这些量子不变量与经典拓扑和几何相关的关键问题。该项目将对低维拓扑学产生重大影响，并在数学和数学物理之间建立深刻而意想不到的联系。