Cosimplicial spaces: applications

Abstract

The homotopy spectral sequence of a cosimplicial space is one of the most commonly used tools in homotopy theory. It first appeared in the work of Bousfield and Kan [14] and has been further analyzed by Bousfield [10]. Two of the standard examples include the Bousfield-Kan spectral sequence — an unstable Adams spectral sequence that arose before the general example [7] — and the spectral sequence for computing the homotopy groups of the homotopy inverse limit of a diagram of pointed spaces. The main purpose of this chapter is to define and discuss this spectral sequence, and outline some of its applications.KeywordsSpectral SequenceHomotopy GroupInverse LimitWeak EquivalenceForgetful FunctorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.