3-Manifolds with abelian embeddings in $S^4$

Abstract

We consider embeddings of 3-manifolds in $S^4$ such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle $M$ has such an embedding if and only if ${\pi }_1(M{)}^{\prime }$ is perfect, and that the embedding is then essentially unique.

v2 has new theorem on embeddings of mapping tori. Section headings changed, and some reorganization. v3 has two new theorems on the higher rank cases $\beta =4$ and 6, in \S6. v4: Lemma 7 corrected and \S3 rewritten. v5: \S7 rewritten

References in corpus (2)

• Annulus twist and diffeomorphic 4-manifolds
• Complements of connected hypersurfaces in $S^4$