## 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 $$\pi_1(M)'$$ is perfect, and that the embedding is then essentially unique.

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

: Primary 57N13.

This paper is available as a pdf (396kB) file. It is also on the arXiv: arxiv.org/abs/1707.00376.

 Saturday, July 29, 2017