Consider a compact quantum group $G$ acting on an operator algebra $A$. The local triviality dimension of the action is a numerical invariant introduced by Gardella, Hajac, Tobolski and Wu as a non-commutative analogue of the so-called Schwarz genus of the action in the classical case, when $G$ is a plain compact group and $A$ consists of the continuous functions on a compact Hausdorff space $X$: the smallest number of open sets covering $X/G$ and trivializing the bundle $X \to X/G$. We give examples of dimension computations for various classes of actions (e.g. gauge actions on graph $C^*$-algebras) and discuss phenomena that distinguish the non-commutative version of this story from its classical counterpart.

(joint w/ Benjamin Passer and Mariusz Tobolski)