Interactions between geometric and topological structures

几何结构和拓扑结构之间的相互作用

• 批准号: FT170100316
• 负责人: Prof Stephan Tillmann
• 金额: $ 57.69万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT170100316
• 关键词: Interactions; between; geometric; topological; structures

This project aims to develop the necessary tools for a geometric imagination in higher dimensions and to bridge the gap between low and high dimensions. Topology is the mathematical study of the shape of spaces. Geometry endows spaces with additional structure such as distance, angle and curvature. Moduli space encodes the different ways in which a geometry can be assigned to a space. Expected outcomes of the project include construction of computable invariants, solution of realisation problems and understanding degeneration of geometries.

该项目旨在开发必要的工具，以在更高的维度上产生几何想象力，并弥合低维度和高维度之间的差距。拓扑是对空间形状的数学研究。几何形状赋予了其他结构，例如距离，角度和曲率。 Moduli空间编码将几何形状分配到空间的不同方式。该项目的预期结果包括构建可计算的不变性，实现问题的解决方案以及理解几何形状的变性。