Topology of toric spaces

复曲面空间的拓扑

• 批准号: 371624-2009
• 负责人: Franz, Matthias
• 金额: $ 1.68万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=528300
• 关键词: Topology; toric; spaces

The aim of this project is to investigate the topology of spaces with an action of a torus T=(S^1)^n, the n-fold Cartesian product of a circle. The focus will be on spaces with rich additional structure arising in various fields, e.g., Hamiltonian T-manifolds (symplectic geometry) or toric varieties (algebraic geometry). This is motivated by the fact that algebraic topology, in particular equivariant cohomology, often plays a crucial role in applications of these spaces, for instance to representation theory and combinatorics.

这个项目的目的是研究具有环面T=（S^1）^n（圆的n重笛卡尔积）作用的空间的拓扑。重点将放在各种领域中出现的具有丰富附加结构的空间上，例如，哈密顿T流形（辛几何）或复曲面簇（代数几何）。这是因为代数拓扑，特别是等变上同调，在这些空间的应用中经常扮演着至关重要的角色，例如表示论和组合学。