Stable rank of $mathrm{C}(X)rtimesGamma$

It is shown that, for an arbitrary free and minimal $mathbb Z^n$-action on a compact Hausdorff space $X$, the crossed product C*-algebra $mathrm{C}(X)rtimesmathbb Z^n$ always has stable rank one, i.e., invertible elements are dense. This generalizes a result of Alboiu and Lutley on $mathbb Z$-actions. In fact, for any free and minimal topological dynamical system $(X, Gamma)$, where $Gamma$ is a countable discrete amenable group, if it has the uniform Rokhlin property and Cuntz comparison of open sets, then the crossed product C*-algebra $mathrm{C}(X)rtimesGamma$ has stable rank one. Moreover, in this case, the C*-algebra $mathrm{C}(X)rtimesGamma$ absorbs the Jiang-Su algebra tensorially if, and only if, it has strict comparison of positive elements.