Cohomology and Actions of Finite Groups

DMS-9987434 Alejandro Adem在这个项目中，主要研究者建议使用代数和拓扑方法来研究变换群，群上同调和相关主题中的一些基本问题。特别是他建议研究现象的周期性群上同调通过组行动;分析上同调的某些伽罗瓦集团所产生的基本问题，在外地理论;计算上同调的低秩零星简单的群体;并研究一些代数和拓扑学之间明显相互作用的杂项问题。拓扑学测量数学对象的不变的内在性质在扭曲和拉伸的变形下特别是对称性可以卓有成效地研究使用拓扑方法。例子来自物理学以及其他自然科学，获得精确的数学方法进行研究是一个具有挑战性的课题。该项目建议使用最近开发的数学技术以及计算机辅助计算来实现这一点，在许多不同的情况下，这是众所周知的重大利益。

DMS-9987434Alejandro AdemIn this project the principal investigator proposes to use both algebraic and topological methods to study a number of basic questions in transformation groups, group cohomology and related topics. In particular he proposes to study the phenomenon of periodicity in group cohomology via group actions; to analyze the cohomology of certain Galois groups arising from basic questions in field theory; to calculate the cohomology of low rank sporadic simple groups; and to investigate a number of miscellaneous problems where a significant interplay of algebra and topology is apparent.Topology measures intrinsic properties of mathematical objects which are invariant under deformations like twisting and pulling. In particular symmetries can be fruitfully studied by using topological methods. Examples arise from physics as well as other natural sciences and obtaining precise mathematical methods for their study is a challenging topic. This project proposes to use recently developed mathematical techniques as well as computer assisted calculations to achieve this in anumber of different instances which are known to be of significant interest.