Graphs of groups

dc.contributorDixon, Martyn R.
dc.contributorEvans, Martin J.
dc.contributorTrace, Bruce S.
dc.contributorLiem, Vo T.
dc.contributorWright, Vivian H.
dc.contributor.advisorCorson, Jon M.
dc.contributor.authorGreen, Michael Timothy
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-03-01T16:25:09Z
dc.date.available2017-03-01T16:25:09Z
dc.date.issued2012
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractGraphs of groups were first introduced by Jean-Pierre Serre in his book entitled Arbres, Amalgames, SL2 (1977), whose first English translation was Trees in 1980. In 1993, Hyman Bass wrote a paper called Covering theory for graphs of groups which discussed such concepts in the category of Graphs of Groups as morphisms, fundamental groups, and infinite covers. Hence, this area of geometric group theory is typically referred to as Bass-Serre Theory. The contents of this dissertation lie within this broad area of study. The main focus of the research is to try to apply to the category of Graphs of Groups what John Stallings did in the category of Graphs in his paper Topology of finite graphs. In that paper, he explored in graphs a vast number of topics such as pullbacks, paths, stars, coverings, and foldings. The goal of this dissertation is to apply many of those concepts to the category of Graphs of Groups. In this work, we develop our notion of paths, links, maps of graphs of groups, and coverings. We then explore the resultant path-lifting properties.en_US
dc.format.extent82 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0000862
dc.identifier.otherGreen_alatus_0004D_11078
dc.identifier.urihttps://ir.ua.edu/handle/123456789/1364
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleGraphs of groupsen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.
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