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 mapsâ€¦ (More)

We develop a general theory of cosimplicial resolutions, homotopy spectral sequences, and completions for objects in model categories, extending work of Bous eld{Kan and Bendersky{Thompson forâ€¦ (More)

For each cosimplicial simplicial set with basepoint, the authors construct a homotopv soectral sequence generalizing the usual spectral sequence for a second quadrant double chain complex. For suchâ€¦ (More)

Smash and composition pairings, as well as Whitehead products are constructed in the unstable Adams spectral sequence; and these pairings and products are described homologically on the E level. Inâ€¦ (More)

In the 1980's, remarkable advances were made by Ravenel, Hopkins, Devinatz, and Smith toward a global understanding of stable homotopy theory, showing that some major features arise "chromatically"â€¦ (More)

We determine the 2-adic K-localizations for a large class of Hspaces and related spaces. As in the odd primary case, these localizations are expressed as bers of maps between speci ed in nite loopâ€¦ (More)

In telescopic homotopy theory, a space or spectrum X is approximated by a tower of localizations LnX, n â‰¥ 0, taking account of vn-periodic homotopy groups for progressively higher n. For each n â‰¥ 1,â€¦ (More)

Let U denote the category of unstable modules over the mod 2 Steenrod algebra A, and let Ext(âˆ’) = ExtsU(âˆ’,Î£Z2). Let Mâˆž = HÌƒâˆ—(Î£CPâˆž + ) denote the unstable A-module with nonzero classes xi such that iâ€¦ (More)