Vol. 39, No. 3, 1971

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Planar surfaces in knot manifolds

Howard Wilson Lambert

Vol. 39 (1971), No. 3, 727–733

Let K be a knot manifold, that is the 3-sphere Ss minus an open regular neighborhood of a polygonal simple closed curve in ∕Ss. Whether K can be embedded in S8 differently or in a homotopy 3-sphere different from S8 (if such really exist) leads in a natural way to the question of which planar surfaces can be embedded in K. Geometric conditions are imposed on the embedded planar surfaces which are sufficient to imply that K is not knotted, that is K is homeomorphic to a disk cross S1.

Mathematical Subject Classification
Primary: 55A25
Received: 30 September 1970
Revised: 14 February 1971
Published: 1 December 1971
Howard Wilson Lambert