Homotopy Theoretic Methods in Group Cohomology

Abstract

This book looks at group cohomology with tools that come from homotopy theory.These tools give both decomposition theorems (which rely on homotopy colimitsto obtain a description of the cohomology of a group in terms of thecohomology of suitable subgroups) and global structure theorems (which exploitthe action of the ring of topological cohomology operations). The approach isexpository and thus suitable for graduate students and others who would likean introduction to the subject that organizes and adds to the relevantliterature and leads to the frontier of current research. The book should alsobe interesting to anyone who wishes to learn some of the machinery of homotopytheory (simplicial sets, homotopy colimits, Lannes' T-functor, the theory ofunstable modules over the Steenrod algebra) by seeing how it is used in apractical setting.