On 4-dimensional flows with wildly embedded invariant manifolds of a periodic orbit

In the present paper we construct an example of 4-dimensional flows on 𝕊³ × 𝕊¹ whose saddle periodic orbit has a wildly embedded 2-dimensional unstable manifold. We prove that such a property has every suspension under a non-trivial Pixton's diffeomorphism. Moreover we give a complete topological classification of these suspensions.