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 |
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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 |
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