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

By John H. Palmieri

We observe the instruments of reliable homotopy thought to the learn of modules over the mod $p$ Steenrod algebra $A^{*}$. extra accurately, enable $A$ 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 sturdy homotopy classification, to be able to use Brown representability, Bousfield localization, Brown-Comenetz duality, and different homotopy-theoretic instruments to check it. One concentration of cognizance is the analogue of the good homotopy teams of spheres, which during this surroundings is the cohomology of $A$, $\mathrm{Ext}_A^{**}(\mathbf{F}_p,\mathbf{F}_p)$. We even have nilpotence theorems, periodicity theorems, a convergent chromatic tower, and several effects.

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