Algebraic Topology

代数拓扑

• 批准号: 0071482
• 负责人: Randy McCarthy
• 金额: $ 7.5万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071482&HistoricalAwards=false
• 关键词: Algebraic; Topology

DMS-0071482Randy McCarthy (PI)Matthew Ando (co-PI)A fundamental idea in algebraic topology is to study topological spaces by attaching to them algebraic structures which are invariant under deformations. A good structure will often produce profound relationships with other areas of mathematics. Ando and McCarthy propose to investigate problems involving three suchstructures, elliptic cohomology, algebraic K-theory, and the calculus of functors. Ando proposes several projects involving elliptic cohomology, which provides a relationship between topology, algebraic geometry, and string theory. For example, he proposes a new approach to therigidity theorems for elliptic genera, based on the algebraic theory of theta functions. McCarthy plans to further pursue his already successful program of using the calculus of functors to betterunderstand algebraic K-theory. For example, he hopes that ideas from the calculus of functors will clarify Neeman's K-theory of triangluated categories. Ando and McCarthy also plan a joint project toinvestigate the role of the calculus of functors in the new homotopy theory of schemes of Voevodsky and others.

DMS-0071482 Randy McCarthy（PI）Matthew Ando（co-PI）代数拓扑学的一个基本思想是通过在拓扑空间上附加在变形下不变的代数结构来研究拓扑空间。 一个好的结构通常会与数学的其他领域产生深刻的关系。 安藤和麦卡锡建议调查的问题涉及三个suchstructures，椭圆上同调，代数K理论，和演算的函子。 安藤提出了几个涉及椭圆上同调的项目，椭圆上同调提供了拓扑、代数几何和弦理论之间的关系。 例如，他提出了一种新的方法，therigidity定理椭圆属，根据代数理论的θ函数。麦卡锡计划进一步追求他已经成功的计划，使用函子演算来更好地理解代数K理论。 例如，他希望从函子演算的想法将澄清尼曼的K-理论的三角范畴。 安藤和麦卡锡还计划一个联合项目，以调查作用的演算函子在新同伦理论的计划Voevodsky和其他人。