Invariant knots of free involutions of \(S^ 4\) (Q2266268)

Given a free involution of a homotopy 4-sphere, the author shows that any 2-spheres invariant under the involution are not only concordant but equivariantly concordant; this result being valid in the topological or smooth \((=PL)\) categories. En route to this result he shows that any smooth s-cobordism with both ends diffeomorphic to a given homotopy \({\mathbb{R}}P^ 4\) is in fact diffeomorphic to a product. Finally he gives an explicit construction for the unique non-smooth homotopy \({\mathbb{R}}P^ 4\).