Homology for higher-rank graphs and twisted \(C^*\)-algebras (Q452361)

The authors introduce a homology theory for higher rank graphs modelled on the cubical version of singular homology, and exhibit combinatorial versions of a number of standard topological constructions. They show that the homology of a higher rank graph coincides with the singular homology of its topological realization. For a higher rank graph, the authors define the \(C^*\)-algebra twisted by a circle-valued cocycle, and show that its isomorphism class depends only on the cohomology class of the cocycle. They also consider some interesting examples.