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

Abstract

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. In order to construct singular Seifert surfaces for the immersions, we use the Kirby calculus.

arXiv comment19 pages, 17 figures

References in corpus (3)

• Canonical framings for 3-manifolds
• Sphere eversions and realization of mappings
• Singular Seifert surfaces and Smale invariants for a family of 3-sphere immersions