Stable Homotopy over the Steenrod Algebra - Couverture souple

Palmieri, John H.

Couverture souple

ISBN 10 : 0821826689 ISBN 13 : 9780821826683

Editeur : American Mathematical Society, 2001

Synopsis

We apply the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A^{*}$. More precisely, let $A$ be the dual of $A^{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective co modules over $A$, in which the morphisms are cochain homotopy classes of maps. This category is triangulated. Indeed, it is a stable homotopy category, so we can use Brown representability, Bousfield localization, Brown-Comenetz duality, and other homotopy-theoretic tools to study it. One focus of attention is the analogue of the stable homotopy groups of spheres, which in this setting is the cohomology of $A$, $\mathrm{Ext}_A^{**}(\mathbf{F}_p,\mathbf{F}_p)$. We also have nilpotence theorems, periodicity theorems, a convergent chromatic tower, and a number of other results.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2001
• Langue: anglais
• ISBN 10: 0821826689
• ISBN 13: 9780821826683
• Reliure: Poche
• Nombre de pages: 172
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible