Graph Groupoids and their Topology

by 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. "

86 pages, Paperback

Published July 29, 2008