Abstract

We study dimension theory for the C*algebras of rowfinite kgraphs with
no sources. We establish that strong aperiodicity—the higherrank analogue of condition
(K)—for a kgraph is necessary and sufficient for the associated C*algebra to have
topological dimension zero. We prove that a purely infinite 2graph algebra has realrank
zero if and only if it has topological dimension zero and satisfies a homological condition
that can be characterised in terms of the adjacency matrices of the 2graph. We also
show that a kgraph C*algebra with topological dimension zero is purely infinite if and
only if all the vertex projections are properly infinite. We show by example that there are
strongly purely infinite 2graphs algebras, both with and without topological dimension
zero, that fail to have realrank zero.