Topological spaces associated to higher-rank graphs

Kumjian, A., Pask, D., Sims, A. and Whittaker, M. F. (2016) Topological spaces associated to higher-rank graphs. Journal of Combinatorial Theory, Series A, 143, pp. 19-41. (doi: 10.1016/j.jcta.2016.04.005)

Abstract

We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that identifying isomorphic co-hereditary subgraphs in a disjoint union of two rank-k graphs gives rise to pullbacks of the associated C*-algebras. We describe a combinatorial version of the connected-sum operation and apply it to the rank-2-graph realisations of the four basic surfaces to deduce that every compact 2-manifold is the topological realisation of a rank-2 graph. We also show how to construct k-spheres and wedges of k-spheres as topological realisations of rank-k graphs.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Whittaker, Professor Mike
• Authors: Kumjian, A., Pask, D., Sims, A., and Whittaker, M. F.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Journal of Combinatorial Theory, Series A
• Publisher: Elsevier
• ISSN: 0097-3165
• ISSN (Online): 1096-0899
• Copyright Holders: Copyright © 2016 Elsevier
• First Published: First published in Journal of Combinatorial Theory, Series A 143:19-41
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

Related URLs

• arXiv