Download E-books Stable Homotopy over the Steenrod Algebra (Memoirs of the American Mathematical Society) PDF

By John H. Palmieri

We practice the instruments of strong homotopy conception to the learn of modules over the mod $p$ Steenrod algebra $A^{*}$. extra accurately, permit $A$ be the twin of $A^{*}$; then we examine the class $\mathsf{stable}(A)$ of unbounded cochain complexes of injective co modules over $A$, within which the morphisms are cochain homotopy periods of maps. This type is triangulated. certainly, it's a strong homotopy type, so that you can use Brown representability, Bousfield localization, Brown-Comenetz duality, and different homotopy-theoretic instruments to check it. One concentration of realization is the analogue of the strong homotopy teams of spheres, which during this surroundings is the cohomology of $A$, $\mat{Ext}_A^{**}(\mathbf{F}_p,\mathbf{F}_p)$. We even have nilpotence theorems, periodicity theorems, a convergent chromatic tower, and several other effects.

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