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方法，以在低维度和高维度的流形上找到几何和离散结构，并促进我们对物理学提供这些空间提供的信息的理解。最近，在理解3-D空间以及数学物理学（量子不变，弦理论）和此类空间之间的相互作用方面取得了巨大的进步。在这个项目中，第一个目的是使用三角剖分构建具有良好几何特性的结构。第二个目的是使用我们的新技术研究N-manifolds的组合分解，并搜索非阳性曲率的多面体指标。第三个目的是再次使用三角形连接量子不变性和几何结构。