Mathematical Sciences: Applications of Stratified Morse Theory and Intersection Homology

数学科学：分层莫尔斯理论和交集同调的应用

• 批准号: 8802638
• 负责人: R. Mark Goresky
• 金额: --
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802638&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Stratified; Morse

1. Applications of Intersection Homology: A study will be made of the torsion-linking pairing which exists on the intersection homology peripheral group of a complex analytic variety, and, in particular, its relationship with the multiplicity of the characteristic variety will be studied. Piecewise linear differential forms with singularities will be constructed for which the L2 forms compute the intersection homology, on any simplicial complex which can be (P.L) stratified with even-codimension strata. Hecke correspondences which induce homomorphisms on intersection homology will be studied, and their Lefschetz numbers will be calculated using geometric techniques. 2. Applications of Stratified Morse Theory: N. Spaltenstein's conjecture relating the intersection homology of nilpotent varieties and the Poincare polynomial of the complement of certain arrangements of hyperplanes will be investigated using the geometric techniques of stratified Morse theory.

1。相交同源性的应用：将对存在复杂分析多样性的相交同源性外围群中存在的扭转链接配对进行研究，尤其是将其与特征品种的多样性的关系进行研究。 将构建具有奇异性的分段线性差分形式，其中L2形式在任何可以用均匀的构量层分层的简单复合物上计算交点同源性。 将研究诱导相交同源性同态的Hecke对应关系，并将使用几何技术计算其Lefschetz数字。 2。分层摩尔斯理论的应用：N。Spaltenstein的猜想将使用分层的摩尔斯理论的几何技术研究，将nilpotent品种的相交同源性和某些超平面互补的庞加罗多项式进行研究。