Non-existence of a stable homotopy category for p-complete abelian groups
| dc.contributor.author | Vanderpool, Ruth, 1980- | |
| dc.date.accessioned | 2010-03-05T01:33:36Z | |
| dc.date.available | 2010-03-05T01:33:36Z | |
| dc.date.issued | 2009-06 | |
| dc.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. | en_US |
| dc.description.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]. | en_US |
| dc.description.sponsorship | Committee in charge: Hal Sadofsky, Chairperson, Mathematics; Boris Botvinnik, Member, Mathematics; Daniel Dugger, Member, Mathematics; Sergey Yuzvinsky, Member, Mathematics; Elizabeth Reis, Outside Member, Womens and Gender Studies | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/10244 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | University of Oregon | en_US |
| dc.relation.ispartofseries | University of Oregon theses, Dept. of Mathematics, Ph. D., 2009; | |
| dc.subject | Stable homotopy | en_US |
| dc.subject | P-complete abelian groups | en_US |
| dc.subject | Homology functor | en_US |
| dc.subject | Abelian | en_US |
| dc.subject | Mathematics | en_US |
| dc.title | Non-existence of a stable homotopy category for p-complete abelian groups | en_US |
| dc.type | Thesis | en_US |
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