Immersions of 3-sphere into 4-space associated with Dynkin diagrams of types A and D

kinjo; shumi;

We construct two infinite sequences of immersions of the 3-sphere into 4-space, parameterized by the Dynkin diagrams of types A and D. The construction is based on immersions of 4-manifolds obtained as the plumbed immersions along the weighted Dynkin diagrams. We compute their Smale invariants and bordism classes of immersions by using Ekholm–Takase’s formula in terms of singular Seifert surfaces.