Abstract
Andrews and Curtis have shown (1) that one can embed two Sn's in En+2 for n = 2, in such a way that one sphere cannot be shrunk to a point in the residue space of the other. In this paper the result is shown to be true for any n ≥ 1. (The result is obvious for n = 1.) The method is to calculate the appropriate homotopy group of the residue space of one sphere, and to show that the embedding of the other sphere represents a non-zero element of the group. The two spheres can both be embedded analytically.
Publisher
Cambridge University Press (CUP)
Reference3 articles.
1. Zur Isotopie zweidimensionaler Flächen imR 4
2. (1) Andrews J. J. and Curtis M. L. Knotted 2-spheres in the 4-sphere (to appear).
3. On Dehn's Lemma and the Asphericity of Knots
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