Moves on <i>k</i>-graphs preserving Morita equivalence

Abstract We initiate the program of extending to higher-rank graphs ( k -graphs) geometric classification directed graph $C^*$ -algebras, as completed in Eilers et al. (2016, Preprint). To be precise, we identify four “moves,” or modifications, one can perform on a -graph $\Lambda $ , which leave invariant Morita equivalence class its -algebra $C^*(\Lambda )$ . These moves—in-splitting, delay, sink deletion, and reduction—are inspired by moves for described Sørensen (Ergodic Th. Dyn. Syst. 33 (2013), 1199–1220) Bates Pask 24 (2004), 367–382). Because this, our perspective -graphs focuses underlying graph. consequently include two new results, Theorem 2.3 Lemma 2.9, about relationship between