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-0071482RANDY MCCARTHY（PI）MATTHEW ANDO（CO-PI）代数拓扑中的一个基本思想是通过在变形下不变的代数结构附加到代数结构来研究拓扑空间。 良好的结构通常会与其他数学领域产生深远的关系。 安多（Ando）和麦卡锡（McCarthy）提议研究涉及三个这样的结构，椭圆共同体，代数K理论和函子计算的问题。 安多（Ando）提出了涉及椭圆形共同体学的几个项目，该项目提供了拓扑，代数几何学和弦理论之间的关系。 例如，他根据theta函数的代数理论提出了一种新的椭圆属定理方法。麦卡锡计划进一步追求他已经成功的计划，以使用函子的计算来更好地理解代数K理论。 例如，他希望函数计算中的想法能够阐明Neeman的K理论的三角形类别。 安多（Ando）和麦卡锡（McCarthy）还计划了一个联合项目，以对沃文沃德斯基（Voevodsky）方案的新同义理论和其他方案的新同义理论进行评估。