Adrian Wilson

Graph Groupoids and Their Topology Adrian Wilson

The book investigates graph groupoids and the path spaces associated with their unit spaces. Three main questions are solved. For the first, a natural question that was asked by A. Kumjian in the case of the Cuntz graph was how the topological space X relates to an earlier topological spaceinvestigated by J. Renault (Orleans). I show that the two topological spaces are homeomorphic and so can be identified. I then discuss the graph groupoid in the general case. For thisinvestigation, it is important to be able to use the axiomatic approachto groupoids, and I show that this is equivalent to the usual definitionof a groupoid as a small category with inverses". This proof of this equivalence answers the second main question. The last is to construct the graph groupoid and prove that it is a second countable locally compact Hausdorff groupoid. "