RIS ID
107973
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.
Grant Number
ARC/DP120100389
Grant Number
ARC/DP130100490
Publication Details
Kumjian, A., Pask, D., Sims, A. & Whittaker, M. F. (2016). Topological spaces associated to higher-rank graphs. Journal of Combinatorial Theory, Series A, 143 19-41.