Symplectic solvmanifolds and their friends

辛求解流形及其朋友

• 批准号: DE150101647
• 负责人: Dr Wolfgang Globke
• 金额: $ 22.16万
• 依托单位: The University of Adelaide
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE150101647
• 关键词: Symplectic; solvmanifolds; their; friends

Symplectic geometry is the mathematical foundation of classical mechanics and quantum theory. The symmetry group of a physical system determines the conservation laws governing its behaviour. This project aims to advance the understanding of a large class of these symmetry groups and their associated symplectic geometries, which are called symplectic solvmanifolds. The project aims to: determine the topological properties of symplectic solvmanifolds as encoded in their fundamental groups; their geometric properties in the form of holonomy groups; and the algebraic properties of their symplectic algebras. The project endeavours to classify the building blocks of symplectic geometry.

辛几何是经典力学和量子理论的数学基础。物理系统的对称群决定了支配其行为的守恒定律。这个项目的目的是促进了解一大类这些对称群及其相关的辛几何，这是所谓的辛solvmanifold。该项目旨在：确定编码在其基本群的辛解流形的拓扑性质;其几何性质的形式holonomy群;和其辛代数的代数性质。该项目致力于对辛几何的构建块进行分类。