On Knots with Nontrivial Interpolating Manifolds

Jonathan Simon
1971 Transactions of the American Mathematical Society  
If a polygonal knot K in the 3-sphere Sa does not separate an interpolating manifold S for K, then S -K does not carry the first homology of either closed component of S3 -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 S3 and sewing it back differently.
doi:10.2307/1995821 fatcat:lo3pd4vjybcehnyfvazjmcjbou