On knots with nontrivial interpolating manifolds
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- by Jonathan Simon PDF
- Trans. Amer. Math. Soc. 160 (1971), 467-473 Request permission
Abstract:
If a polygonal knot $K$ in the $3$-sphere ${S^3}$ does not separate an interpolating manifold $S$ for $K$, then $S - K$ does not carry the first homology of either closed component of ${S^3} - S$. It follows that most knots $K$ with nontrivial interpolating manifolds have the property that a simply connected manifold cannot be obtained by removing a regular neighborhood of $K$ from ${S^3}$ and sewing it back differently.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 160 (1971), 467-473
- MSC: Primary 55.20
- DOI: https://doi.org/10.1090/S0002-9947-1971-0288753-3
- MathSciNet review: 0288753