p-completions of nilpotent spaces
In this chapter we discuss the p-completion, i.e. the “up to homotopy” version of the Zp-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 Zp-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.
KeywordsAbelian Group Spectral Sequence Nilpotent Group Short Exact Sequence Finite Type
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