3-Manifolds with abelian embeddings in $S^4$
Geometric Topology
2021-02-24 v5
Abstract
We consider embeddings of 3-manifolds in such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle has such an embedding if and only if is perfect, and that the embedding is then essentially unique.
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