# Graphs of groups

 dc.contributor Dixon, Martyn R. dc.contributor Evans, Martin J. dc.contributor Trace, Bruce S. dc.contributor Liem, Vo T. dc.contributor Wright, Vivian H. dc.contributor.advisor Corson, Jon M. dc.contributor.author Green, Michael Timothy dc.date.accessioned 2017-03-01T16:25:09Z dc.date.available 2017-03-01T16:25:09Z dc.date.issued 2012 dc.identifier.other u0015_0000001_0000862 dc.identifier.other Green_alatus_0004D_11078 dc.identifier.uri https://ir.ua.edu/handle/123456789/1364 dc.description Electronic Thesis or Dissertation dc.description.abstract Graphs 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. dc.format.extent 82 p. dc.format.medium electronic dc.format.mimetype application/pdf dc.language English dc.language.iso en_US dc.publisher University of Alabama Libraries dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations dc.relation.ispartof The University of Alabama Libraries Digital Collections dc.relation.hasversion born digital dc.rights All rights reserved by the author unless otherwise indicated. dc.subject.other Mathematics dc.title Graphs of groups dc.type thesis dc.type text etdms.degree.department University of Alabama. Dept. of Mathematics etdms.degree.discipline Mathematics etdms.degree.grantor The University of Alabama etdms.degree.level doctoral etdms.degree.name Ph.D.
﻿