deleanu, frei, and hilton have developed the notion of generalized adams completion in a categorical context. in this paper, we have obtained the postnikov-like approximation of a module, with the help of a suitable set of morphisms.

Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.

The behavior of fibrewise localization and completion on the classifying space level is analyzed. The relationship of these constructions to fibrewise joins and smash products and to orientations of spherical fibrations is also analyzed. This theory is essential to validate Sullivan's proof of the Adams conjecture. In Sullivan's beautiful proof of the Adams conjecture [20], perhaps the crucial ...

We investigate Γ-cohomology of some commutative cooperation algebras E∗E associated with certain periodic cohomology theories. For KU and E(1), the Adams summand at a prime p, and for KO we show that Γ-cohomology vanishes above degree 1. As these cohomology groups are the obstruction groups in the obstruction theory developed by Alan Robinson we deduce that these spectra admit unique E∞ structu...

We refine our earlier work on the existence and uniqueness of E∞ structures on K-theoretic spectra to show that at each prime p, the connective Adams summand ℓ has an essentially unique structure as a commutative S-algebra. For the p-completion ℓp we show that the McClure-Staffeldt model for ℓp is equivalent as an E∞ ring spectrum to the connective cover of the periodic Adams summand Lp. We est...