English

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

Geometric Topology 2021-02-24 v5

Abstract

We consider embeddings of 3-manifolds in S4S^4 such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle MM has such an embedding if and only if π1(M)\pi_1(M)' is perfect, and that the embedding is then essentially unique.

Keywords

Cite

@article{arxiv.1707.00376,
  title  = {3-Manifolds with abelian embeddings in $S^4$},
  author = {J. A. Hillman},
  journal= {arXiv preprint arXiv:1707.00376},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-22T20:35:47.787Z