Quantum invariants and hyperbolic manifolds in three-dimensional topology

三维拓扑中的量子不变量和双曲流形

• 批准号: DP160103085
• 负责人: Prof Jessica Purcell
• 金额: $ 31.42万
• 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: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-05-13 至 2020-09-10
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP160103085
• 关键词: Quantum; invariants; hyperbolic; manifolds; three

The project aims to broaden our understanding of three-dimensional (3-D) spaces, including spaces that arise in engineering, microbiology and physics. It is known that all 3-D spaces can be decomposed into geometric pieces. The most common type of geometry is hyperbolic. It is also known that such spaces have algebraic structures arising from quantum physics, known as quantum invariants. Several important conjectures, based on developments in physics, assert that hyperbolic geometry and quantum invariants are deeply related, but they remain unproved. The project aims to find new relationships between hyperbolic geometry and quantum invariants, advancing our understanding of both areas.

该项目旨在扩大我们对三维（3-D）空间的理解，包括工程，微生物学和物理学中出现的空间。众所周知，所有的三维空间都可以分解成几何碎片。最常见的几何类型是双曲型。我们还知道，这样的空间具有量子物理学中的代数结构，称为量子不变量。基于物理学发展的几个重要理论断言双曲几何和量子不变量有很深的联系，但它们仍未得到证明。该项目旨在寻找双曲几何和量子不变量之间的新关系，推进我们对这两个领域的理解。