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Infinitely many disk knots with the same exterior

Published online by Cambridge University Press:  24 October 2008

Steven P. Plotnick
Steven P. Plotnick
Affiliation:
Columbia University, New York
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Extract

This paper addresses the question of how well the exterior of a knot determines the knot. It is well known that for a knotted sphere pair (Sn+2, Sn), n ≥ 2, a given exterior corresponds to at most two distinct knots (1), (4), (10); examples of distinct knots with the same exterior are given in (2), (6). For a knotted ball pair (Bn+2, Bn), n ≥ 2, the situation may be more complicated. In fact, given an arbitrary positive integer N, Hitt-Sumners (7), (8) constructed N distinct ball pairs with the same exterior, n ≥ 4.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 67 - 72
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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