3-Manifolds with abelian embeddings in \(S^4\)



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.

AMS Subject Classification: Primary 57N13.

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Saturday, July 29, 2017