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. Intersection Homology的应用： 本文将研究存在于 复解析的交同调周边群 多样性，特别是它与多样性的关系。 将研究的特征品种。 具有奇异性的分段线性微分形式将是 L2形式计算其交集 同调，在任何可以（P.L）分层的单纯复形上 偶余维地层 上诱导同态的Hecke对应 将研究相交同调，及其莱夫谢茨数 将使用几何技术计算。 2. 分层莫尔斯理论的应用： N.关于的交同调的Spalanche猜想 幂零簇与补的Poincare多项式 超平面的某些安排将使用 分层莫尔斯理论的几何技术。