Abstract

We initiate the program of extending to higherrank graphs ($k$graphs) the
geometric classification of directed graph $C^*$algebras, as completed in the
2016 paper of Eilers, Restorff, Ruiz, and Sorensen [ERRS16]. To be precise, we
identify four "moves," or modifications, one can perform on a $k$graph
$\Lambda$, which leave invariant the Morita equivalence class of its
$C^*$algebra $C^*(\Lambda)$. These moves  insplitting, delay, sink deletion,
and reduction  are inspired by the moves for directed graphs described by
Sorensen [S\o13] and BatesPask [BP04]. Because of this, our perspective on
$k$graphs focuses on the underlying directed graph. We consequently include
two new results, Theorem 2.3 and Lemma 2.9, about the relationship between a
$k$graph and its underlying directed graph.