Graphs of groups

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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.

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