The singular set of group actions on homotopy spheres (Q1064624)

Let G be a finite group. The author studies the question when a G complex A is the singular set (i.e. the set of nonfree orbits) of an action of G on some homotopy sphere X. Actions are assumed to be G cellular. The author gives a list of conditions on A, some necessary and some convenient, in terms of homology and the existence of a G invariance structure (compatibly chosen G invariant models of X, one for each Sylow subgroup of G). Assuming data which satisfy these conditions, A can be realized as singular set of a G action on a homotopy sphere. The paper improves the author's earlier results [Invent. Math. 67, 231-252 (1982; Zbl 0507.57026)]. The problem of realizing a G complex as singular set of an action on a disk has been studied previously by Oliver, Oliver- \(Petrie\), and Assadi.