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Infinitely many ribbon knots with the same fundamental group

Published online by Cambridge University Press:  24 October 2008

Alexander I. Suciu
Alexander I. Suciu
Affiliation:
Department of Mathematics, Yale University, New Haven, CT 06520
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We work in the DIFF category. A knot K = (Sn+2, Sn) is a ribbon knot if Sn bounds an immersed disc Dn+1 →Sn+2 with no triple points and such that the components of the singular set are n-discs whose boundary (n – l)-spheres either lie on Sn or are disjoint from Sn. Pushing Dn+1 into Dn+3 produces a ribbon disc pair D = (Dn+3, Dn+1), with the ribbon knot (Sn+2, Sn) on its boundary. The double of a ribbon (n+1)-disc pair is an (n + l)-ribbon knot. Every (n+l)-ribbon knot is obtained in this manner.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 3 , November 1985 , pp. 481 - 492
Copyright
Copyright © Cambridge Philosophical Society 1985

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