Embedding homology 3-spheres in S⁵

Steven Paul Plotnick

Vol. 101 (1982), No. 1, 147–151

DOI: 10.2140/pjm.1982.101.147

Abstract

The purpose of this note is to give a proof independent of high-dimensional surgery theory of the following embedding result:

Theorem. Let Σ³ be the homology 3-sphere resulting from a Dehn surgery of type 1∕2a on a knot in S³. Then Σ³ smoothly embeds in S⁵ with complement a homotopy circle.

Mathematical Subject Classification 2000

Primary: 57R40

Milestones

Received: 1 June 1980

Published: 1 July 1982