Graph Groupoids and their Topology (Paperback) (ISBN-13: 9783639007480)

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 space investigated 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 this investigation, it is important to be able to use the axiomatic approach to groupoids, and I show that this is equivalent to the usual definition of 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.

Author: Adrian Wilson
ISBN-10: 3639007484
ISBN-13: 9783639007480
Publisher: VDM Verlag Dr. Mueller E.K.
Language: English
Published: 07/30/2008
Pages: 84
Format: Paperback
Weight: 0.27lbs
Size: 9.00h x 6.00w x 0.17d