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)

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)

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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, Dr Michael
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
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