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A simplicial homotopy group model for K2 of a ring

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dc.contributor.authorWhitfield, JaDon Saeed, author
dc.contributor.authorDuflot, Jeanne, advisor
dc.contributor.authorMiranda, Rick, committee member
dc.contributor.authorAchter, Jeffrey D., committee member
dc.contributor.authorGelfand, Martin Paul, committee member
dc.date.accessioned2007-01-03T04:55:10Z
dc.date.available2007-01-03T04:55:10Z
dc.date.issued2010
dc.description.abstractWe construct an isomorphism between the group K2(R) from classical, algebraic K-Theory for a ring R and a simplicial homotopy group constructed using simplicial homotopy theory based on that same ring R. First I describe the basic aspects of simplicial homotopy theory. Special attention is paid to the use of category theory, which will be applied to the construction of a simplicial set. K-Theory for K0(R), K1(R) and K2(R) is then described before we set to work describing explicitly the nature of isomorphisms for K0(R) and K1(R) based on previous work. After introducing some theory related to K-Theory, some considerations and corrections on previous work motivate more new theory that helps the isomorphism with K2(R). Such theory is developed, mainly with regards to finitely generated projective modules over R and then elementary matrices with entries from R, culminating in the description of the Steinberg Relations that are central to the understanding of K2(R) in terms of homotopy classes. We then use new considerations on the previous work to show that a map whose image is constructed through this article is an isomorphism since it is the composition of isomorphisms.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierWhitfield_colostate_0053A_10208.pdf
dc.identifierETDF2010100008MATH
dc.identifier.urihttp://hdl.handle.net/10217/45975
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectalgebra
dc.subjecttopology
dc.subjectsimplicial homotopy
dc.subjectHomotopy groups
dc.subjectK-theory
dc.subjectLoop spaces
dc.subjectIsomorphisms (Mathematics)
dc.titleA simplicial homotopy group model for K2 of a ring
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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