| Graph Groupoids and their Topology Contributor(s): Wilson, Adrian (Author) |
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ISBN: 3639007484 ISBN-13: 9783639007480 Publisher: VDM Verlag Dr. Mueller E.K. OUR PRICE: $50.27 Product Type: Paperback Published: July 2008 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics |
| Physical Information: 0.17" H x 6" W x 9" (0.27 lbs) 84 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
