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.