Mathematical Sciences: Geometric Questions in Algebraic Topology

数学科学：代数拓扑中的几何问题

• 批准号: 8901879
• 负责人: Benjamin Mann
• 金额: --
• 依托单位: Clarkson University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1989-07-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901879&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Questions; Algebraic

8901879 Mann Professor Mann will investigate two projects in algebraic topology which, in addition to their topological interest, have applications in mathematical physics, non-linear partial differential equations, and linear control theory. The first project, representing joint work with Professor C. P. Boyer, continues the ongoing program of Professors Boyer and Mann to study the geometry and topology of moduli spaces of instantons and monopoles which arise in the differential geometric formulation of Yang-Mills-Higgs gauge theories. The techniques developed in this program have applications to other moduli problems which will also be investigated. The second project, representing joint work with Professor R.J. Milgram, attempts to extend the results of Professors F.R. Cohen, R.L. Cohen, B.M. Mann, and R.J. Milgram on the more general case of rational functions from the Riemann sphere to Grassmannians and flag manifolds. The topology of such spaces is important in several areas, including linear control theory, and the results of this project will be useful in applications to other areas of mathematics.

8901879曼教授将研究代数拓扑学中的两个项目，除了它们的拓扑兴趣之外，它们还在数学物理中有应用，非线性偏微分方程组和线性控制理论。第一个项目是与C.P.Boyer教授的合作，继续Boyer和Mann教授正在进行的计划，研究杨-Mills-Higgs规范理论的微分几何公式中出现的瞬子和单极子的模空间的几何和拓扑。在本程序中开发的技术也适用于其他模问题，这些问题也将被研究。第二个项目是与R.J.Milgram教授的联合工作，试图将F.R.Cohen、R.L.Cohen、B.M.Mann和R.J.Milgram教授关于有理函数的更一般情况的结果从Riemann球面推广到Grassmannians和国旗流形。这种空间的拓扑在几个领域都很重要，包括线性控制理论，这个项目的结果将在其他数学领域的应用中有用。