Completions and localizations.- The R-completion of a space.- Fibre lemmas.- Tower lemmas.- An R-completion of groups and its relation to the R-completion of spaces.- R-localizations of nilpotent… Expand

IN [8] WE studied localizations of spaces with respect to homology, and we now develop the analogous stable theory. Let Ho” denote the stable homotopy category of CW-spectra. We show that each… Expand

In [2] we constructed homological localizations of spaces, groups, and 17"modules; here we generalize those constructions to give "factorization systems" and "homotopy factorization systems" for maps… Expand

In this paper, we develop a hierarchy of natural localizations of spaces, called the vn-periodizations for n > 0, which may be used to expose and study periodic phenomena in unstable homotopy theory.… Expand

For a pointed cosimplicial spaceX•, the author and Kan developed a spectral sequence abutting to the homotopy of the total space TotX•. In this paper,X• is allowed to be unpointed and the spectral… Expand