Non-existence of a stable homotopy category for p-complete abelian groups
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Date
2009-06
Authors
Vanderpool, Ruth, 1980-
Journal Title
Journal ISSN
Volume Title
Publisher
University of Oregon
Abstract
We investigate the existence of a stable homotopy category (SHC) associated to the category of p -complete abelian groups [Special characters omitted]. First we examine [Special characters omitted] and prove [Special characters omitted] satisfies all but one of the axioms of an abelian category. The connections between an SHC and homology functors are then exploited to draw conclusions about possible SHC structures for [Special characters omitted]. In particular, let [Special characters omitted] denote the category whose objects are chain complexes of [Special characters omitted] and morphisms are chain homotopy classes of maps. We show that any homology functor from any subcategory of [Special characters omitted] containing the p-adic integers and satisfying the axioms of an SHC will not agree with standard homology on free, finitely generated (as modules over the p -adic integers) chain complexes. Explicit examples of common functors are included to highlight troubles that arrise when working with [Special characters omitted]. We make some first attempts at classifying small objects in [Special characters omitted].
Description
vii, 54 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.
Keywords
Stable homotopy, P-complete abelian groups, Homology functor, Abelian, Mathematics