Invariants, geometric and discrete structures on manifolds.

流形上的不变量、几何和离散结构。

• 批准号: DP160104502
• 负责人: Prof Joachim Rubinstein
• 金额: $ 23.41万
• 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: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-03-02 至 2019-06-14
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP160104502
• 关键词: Invariants; geometric; discrete; structures; manifolds.

This project aims to develop practical methods for finding geometric and discrete structures on manifolds in both low and high dimensions and advancing our understanding of the information that physics is providing about these spaces. Recently there have been spectacular advances in understanding 3-D spaces and the interaction between ideas in mathematical physics (quantum invariants, string theory) and such spaces. In this project, the first aim is to construct structures with good geometric properties on 3- and 4-manifolds, using triangulations. The second aim is to study combinatorial decompositions of n-manifolds, using our new technique of multisections and also searching for polyhedral metrics of non-positive curvature. The third aim is to connect quantum invariants and geometric structures, again using triangulations.

该项目旨在开发实用的方法，以寻找低维和高维流形上的几何和离散结构，并促进我们对物理学提供的有关这些空间的信息的理解。最近，在理解三维空间以及数学物理学（量子不变量、弦理论）和三维空间之间的相互作用方面取得了惊人的进展。在这个项目中，第一个目标是使用三角剖分在3-和4-流形上构造具有良好几何性质的结构。第二个目的是研究组合分解的n-流形，使用我们的新技术的多节，也寻找多面体度量的非正曲率。第三个目标是连接量子不变量和几何结构，同样使用三角剖分。