A Note on Embedding Homology 3-Spheres in the 4-Sphere

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 M...

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Bibliographic Details
Published inKyungpook mathematical journal Vol. 64; no. 3; pp. 505 - 509
Main Author Min Hoon Kim
Format Journal Article
LanguageKorean
Published 2024
Subjects
Brieskorn homology 3-spheres
contractible 4-manifolds
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Summary: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.
Bibliography:KISTI1.1003/JNL.JAKO202431243269692
ISSN:1225-6951
0454-8124