Complements of connected hypersurfaces in $S^4$

Jonathan A. Hillman

doi:10.1142/S0218216517400144

Complements of connected hypersurfaces in $S^4$

Geometric Topology 2021-02-24 v4

Authors: Jonathan A. Hillman

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Abstract

We consider the possible Euler characteristics and fundamental groups of the complementary components $X$ and $Y$ of an embedding of a connected closed 3-manifold $M$ in $S^4$ . We use a 2-knot satellite construction to change the fundamental groups, and Massey products to limit the values of $\chi(X)$ and $\chi(Y)$ when $M$ is the total space of an $S^1$ -bundle with orientable base and Euler number 1.

Keywords

hypersurfaces S^4 Euler characteristic fundamental group 3-manifold 2-knot satellite construction Massey products S^1-bundle

Cite

@article{arxiv.1502.04385,
  title  = {Complements of connected hypersurfaces in $S^4$},
  author = {Jonathan A. Hillman},
  journal= {arXiv preprint arXiv:1502.04385},
  year   = {2021}
}

Comments

v2: abstract rewritten and dedication added. More details given for Massey product and surgery arguments. Theorem 7 deleted. v3: reorganised, new results and examples. v4: Section 4 split: new theorem and figure in the new Section 5

Complements of connected hypersurfaces in $S^4$

Abstract

Keywords

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