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

J.A.Hillman

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.

Keywords: abelian embedding, bipartedly trivial link, homology handle, 3-manifold,surgery.

AMS Subject Classification: Primary 57N13.