3-Manifolds with nilpotent embeddings in S4

Abstract

We consider embeddings of 3-manifolds [Formula: see text] in [Formula: see text] such that the two complementary regions [Formula: see text] and [Formula: see text] each have nilpotent fundamental group. If [Formula: see text] is odd then these groups are abelian and [Formula: see text]. In general [Formula: see text] and [Formula: see text] have 3-generator presentations, and [Formula: see text]. We give two examples illustrating our results.