Cohomology and Actions of Finite Groups

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

DMS-9987434 Alejandro Adem In 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 a number of different instances which are known to be of significant interest.