A Note on Embedding Homology 3-Spheres in the 4-Sphere
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Recently, S¸avk 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.
Abstract
Recently, S¸avk 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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