ON THE EVANS CHAIN COMPLEX

Abstract We elaborate on the construction of the Evans chain complex for higher-rank graph $C^*$ -algebras. Specifically, we introduce a block matrix presentation of the differential maps. These block matrices are then used to identify a wide family of higher-rank graph $C^*$ -algebras with trivial K -theory. Additionally, in the specialised case where the higher-rank graph consists of one vertex, we are able to use the Künneth theorem to explicitly compute the homology groups of the Evans chain complex.