Mathematical Sciences: Cohomologies of Matrix Groups amd Mapping Class Groups

数学科学：矩阵群的上同调和映射类群

• 批准号: 8801986
• 负责人: John Maginnis
• 金额: $ 3.3万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801986&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cohomologies; Matrix; Groups

This project investigates collections of all matrices of certain specific types, viewing the collections as geometric objects. Specifically, it is concerned with the calculation of the cohomology rings of certain matrix groups over the finite field of two elements, with coefficients in this same finite field, and with the application of these results to the detection of torsion classes in the integral homology of the mapping class groups of surfaces. The mapping class groups of surfaces with a single fixed boundary component support a homology operation, or equivalently a double loop space structure, that is little understood. Maginnis plans to obtain information about this homology operation by detecting classes in the homology of matrix groups. These matrix groups will include the upper triangular matrices, a Sylow 2-subgroup of the general linear group, and symplectic matrices and their Sylow 2-subgroups. He also plans to study similar matrix groups over the integers.

这个项目调查所有矩阵的集合， 某些特定类型，将集合视为几何图形 对象 具体而言，它涉及计算 有限环上某些矩阵群的上同调环 域的两个元素，系数在这个相同的有限 领域，并与应用这些结果的检测 映射类的积分同调中的挠类 曲面组。 映射类的曲面组， 单个固定边界分量支持同调运算，或者 相当于一个双循环空间结构，这是小 明白 马金尼斯计划获取有关这方面的信息 同源操作，通过检测类的同源性 矩阵群 这些矩阵组将包括上 三角矩阵，一般线性矩阵的Sylow 2-子群 群和辛矩阵及其Sylow 2-子群。 他 也计划研究类似的矩阵群的整数。