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Some Counterexamples in Link Theory

Published online by Cambridge University Press:  20 November 2018

Dale Rolfsen
Dale Rolfsen*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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This note is concerned specifically with links of two (disjoint) n-spheres in an (n + 2)-manifold M, i.e. embeddings L:Sn + Sn —> M. The links L0 and L1 are isotopic if they are t he ends of a continuous family Li:Sn + Sn —> M (0 ≦ t ≦ 1) of links. They are ambient isotopic or equivalent if there is a continuous family of self-homeomorphisms ht: M—> M (0 ≦ t ≦ 1) such that h0 = identity and h1◯L0 = L1. Ambient isotopic links are isotopic, but not conversely. For example, an isotopy can tie and untie little knots (as in Figure 3) in the components of a link, thus changing the original link into one which is inequivalent to the original.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 4 , August 1974 , pp. 978 - 984
Copyright
Copyright © Canadian Mathematical Society 1974

References

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