p-completions of nilpotent spaces

Abstract

In this chapter we discuss the p-completion, i.e. the “up to homotopy” version of the Z_p-completion, for nilpotent spaces. It turns out that this p-completion is closely related to the p-profinite completion of [Quillen (PG)] and [Sullivan, Ch.3]; indeed, one can show that these completions coincide for spaces with Z_p-homology of finite type, although they differ for more general spaces. The basic properties of p-profinite completions are well-known for simply connected spaces of finite type, and the main purpose of this chapter is to obtain similar results for p-completions of arbitrary nilpotent spaces.

An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-540-38117-4_16