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.identifier.uri |
http://hdl.handle.net/1794/10244 |
|
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.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 |