Higman–Thompson groups of unfolding trees of rooted graphs

<p dir="ltr">This thesis will discuss unfolding trees (i.e. universal covers) of rooted directed graphs and their almost structure. Using the graph monoid, we will characterize these trees up to almost isomorphism. We will introduce a labelling of a graph that identifies when they are cocompact (and thus identify when a tree is almost isomorphic to a cocompact tree). We will go on to explore the Higman–Thompson group of these trees, showing how connectivity properties determine whether its action on the boundary is minimal, or topologically transitive. This allows us to use results of Nekrashevych[31] to characterize the alternating group. Finally, following the work of Pardo[34] we can embed the Higman–Thompson group into the Leavitt Path algebra and give a sufficient condition for these groups to be isomorphic</p>