Mathematical Sciences: Applications of Intersection Homology

(1)亚瑟和A.塞尔伯格（Selberg） Hecke对应在L2上作用的迹 厄米特局部对称空间的上同调）将是 用Lefschetz不动点的形式加以证明和解释 定理 这将涉及对当地的新评估 在一个固定点上对Lefschetz数的贡献和 一个新的上同调理论（“加权上同调”）的构造 X的约化Borel-Serre紧化 应用 将离散级数特征的计算 表示，离散群的上同调，和霍奇 （p，q）L2上同调的分解。 (2)陈数 奇异复代数簇将通过提升来定义 陈类的交上同调。 不变性 这些新的陈数的性质将被研究。

(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.