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Infinitely many ribbon knots with the same fundamental group

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: A.I. Suciu

Editorial: Mathematical Proceedings of the Cambridge Philosophical Society, 98 (3), p.481-492, 1985.


A knot K = (S^{n+2}, S^n) is a ribbon knot if S^n bounds an immersed disc D^{n+1} in S^{n+2} with no triple points and such that the components of the singular set are n-discs whose boundary (n-1)-spheres either lie on S^n or are disjoint from S^n. Pushing D^{n+1} into D^{n+3} produces a ribbon disc pair D = (D^{n+3}, D^{n+1}), with the ribbon knot (S^{n+2}, S^n) on its boundary. The double of a ribbon (n+1)-disc pair is an (n+1)-ribbon knot. Every (n+1)-ribbon knot is obtained in this manner.

Cuvinte cheie: Knots in the 4-sphere, homotopy groups