Preprint3manifolds with nilpotent embeddings in \(S^4\)J. A. HillmanAbstractWe consider embeddings of 3manifolds \(M\) in \(S^4\) such that the two complementary regions \(X\) and \(Y\) each have nilpotent fundamental group. If \(\beta=\beta_1(M)\) is odd then these groups are abelian and \(\beta\leq3\). In general, \(\pi_1(X)\) and \(\pi_1(Y)\) have 3generator presentations, and \(\beta\leq6\). We determine all such nilpotent groups which are torsionfree and have Hirsch length \(\le5\). Keywords: embedding, homologically balanced, nilpotent, 3manifold, restrained, surgery.AMS Subject Classification: Primary 57N13.
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