Equivariant wedge sum construction of finite contractible \(G\)-CW complexes with \(G\)-vector bundles (Q1567117)

In [Topology 35, No. 3, 583-615 (1996; Zbl 0861.57047)] \textit{B. Oliver} answered the question when a smooth manifold is the fixed point set of a smooth action of a group \(G\) on a disk. The obstruction, beyond those for the construction of such an action in the CW category, is the existence of a certain \(G\)-homotopy commutative diagram. An important step in the construction of the action on a disk is an extension of this diagram. The authors ask whether additional assumptions may be imposed on the action on the disk. In special cases, the authors discuss the extension of the relevant diagram which reflects these additional assumptions.