Topological spaces associated to higher-rank graphs

@article{Kumjian2013TopologicalSA,
  title={Topological spaces associated to higher-rank graphs},
  author={Alex Kumjian and David Pask and Aidan Sims and Michael F. Whittaker},
  journal={J. Comb. Theory, Ser. A},
  year={2013},
  volume={143},
  pages={19-41}
}

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References

SHOWING 1-10 OF 24 REFERENCES

Topological realizations and fundamental groups of higher-rank graphs

Abstract We investigate topological realizations of higher-rank graphs. We show that the fundamental group of a higher-rank graph coincides with the fundamental group of its topological realization.

Higher Rank Graph C-Algebras

Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of

Remarks on some fundamental results about higher-rank graphs and their C*-algebras

Abstract Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the

Fundamental groupoids of k-graphs

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz- Krieger type. Here we develop a theory of the

On higher rank graph C ∗ -algebras

Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C *-algebra, C * (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C

Skew-products of higher-rank graphs and crossed products by semigroups

We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C∗-algebra of the graph. We show that the crossed product by this action is stably

Directed combinatorial homology and noncommutative tori (The breaking of symmetries in algebraic topology)

  • M. Grandis
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2005
This is a brief study of the homology of cubical sets, with two main purposes. First, this combinatorial structure is viewed as representing directed spaces, breaking the intrinsic symmetries of