Mathematical Sciences: Applications of Intersection Homology

数学科学：交集同调的应用

• 批准号: 9001941
• 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: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001941&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Intersection; Homology

(1) The trace formula of J. Arthur and A. Selberg (for the trace of the action of a Hecke correspondence on the L2 cohomology of a Hermitian locally symmetric space) will be reproved and interpreted in terms of the Lefschetz fixed point theorem. This will involve a new evaluation of the local contribution to the Lefschetz number at a fixed point and the construction of a new cohomology theory ("weighted cohomology") on the reductive Borel-Serre compactification of X. Applications will be made to the computation of characters of discrete series representations, the cohomology of discrete groups, and the Hodge (p,q) decomposition of the L2 cohomology. (2) Chern numbers of singular complex algebraic varieties will be defined by lifting Chern classes to intersection cohomology. The invariance properties of these new Chern numbers will be investigated.

（1）J。Arthur和A. Selberg的痕量公式（对于Hecke对应关系对Hermitian局部对称空间的L2共同体的作用的痕迹）将以LEFSCHETZ固定点定理进行重复和解释。 这将涉及对固定点上对Lefschetz数量的本地贡献的新评估，以及对还原性的borel-serre紧凑型X的新共同体理论（“加权共同体”）的构建。将对离散串联表示的字符的计算进行申请。 （2）Chern数量的奇异复合代数品种的数量将通过将Chern类提升为交叉共同体来定义。 这些新的Chern号码的不变性属性将进行研究。