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Stable Homotopy over the Steenrod Algebra

John Harold Palmieri

出版	American Mathematical Soc., 2001
主題	Mathematics / Group TheoryMathematics / Topology
ISBN	08218266899780821826683
URL	http://books.google.com.hk/books?id=2ZLUCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

This title applys the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A DEGREES{*}$. More precisely, let $A$ be the dual of $A DEGREES{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective comodules 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 $A$, $\mathrm{Ext}_A DEGREES{**}(\mathbf{F}_p, \mathbf{F}_p)$. This title also has nilpotence theorems, periodicity theorems, a convergent chromatic tower, and a nu