Concordance of Zₚ×ₚ actions on S⁴

الأصل · EN

We consider locally linear Zₚ x Zₚ actions on the four-sphere. We present simple constructions of interesting examples, and then prove that a given action is concordant to its linear model if and only if a single surgery obstruction taking to form of an Arf invariant vanishes. We discuss the behavior of this invariant under various connected-sum operations, and conclude with a brief discussion of the existence of actions which are not concordant to their linear models.