Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Note on Embedding Homology 3-Spheres in the 4-Sphere

  • Min Hoon Kim (Department of Mathematics, Ewha Womans University)
  • Received : 2024.04.07
  • Accepted : 2024.08.20
  • Published : 2024.09.30
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Abstract

Recently, Şavk introduced the notion of a generalized Mazur manifold, which is a contractible 4-manifold obtained by attaching a 2-handle on the complement of a ribbon disk, and observed that many classical examples of homology 3-spheres bounding contractible 4-manifolds actually bound generalized Mazur manifolds. In this note, we prove that homology 3-spheres bounding generalized Mazur manifolds smoothly embed in the 4-sphere by using 5-dimensional arguments. As a consequence, we show that any homology 3-sphere obtained from the 3-sphere by Dehn surgery on a ribbon link and certain plumbed 3-manifolds smoothly embed in the 4-sphere.

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Acknowledgement

The author was partly supported by Samsung Science and Technology Foundation (SSTF-BA2202-01) and the National Research Foundation grant 2021R1C1C1012939.

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