Homology theories in quantum topology

量子拓扑中的同调理论

• 批准号: DE200100407
• 负责人: Dr Paul Wedrich
• 金额: --
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-12-17 至 2020-12-18
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE200100407
• 关键词: Homology; theories; quantum; topology

This project aims to resolve a major 25-year-old open problem relating the quantum topology of knots, 3- and 4-dimensional spaces to higher representation theory, the study of hidden symmetries of algebraic structures. The project expects to use homological invariants of knots and the higher representation theory of quantum groups to construct highly anticipated invariants of 3- and 4-dimensional manifolds and tools to compute these invariants by reduction to basic building blocks. Expected outcomes also include new connections to diverse areas in mathematics. This is expected to benefit Australian science by invigorating collaboration in mathematics and theoretical physics and by attracting students and distinguished research visitors.

该项目旨在解决一个25年来的重大开放问题，涉及结，3-和4-维空间的量子拓扑结构，更高的表示理论，代数结构的隐藏对称性的研究。该项目预计将使用结的同调不变量和量子群的高级表示理论来构建备受期待的3维和4维流形的不变量，以及通过简化为基本构建块来计算这些不变量的工具。预期成果还包括与数学不同领域的新联系。预计这将通过激发数学和理论物理领域的合作以及吸引学生和杰出的研究访问者而使澳大利亚科学受益。