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Indecomposable knots and concordance

Published online by Cambridge University Press:  24 October 2008

Eva Bayer-Fluckiger  and
Neal W. Stoltzfus
Eva Bayer-Fluckiger
Affiliation:
University of Geneva
Neal W. Stoltzfus
Affiliation:
Louisiana State University
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Extract

R. C. Kirby and W. B. R. Lickorish have proved (cf. (4)) that any classical knot is concordant to an indecomposable knot. In the present note we show that this statement is also true for higher dimensional knots: more precisely, for any higher-dimensional knot K there exist infinitely many non-isotopic indecomposable simple knots which are concordant to K. This, together with the result of Kirby and Lickorish, gives a complete solution of problem 13 of (1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 3 , May 1983 , pp. 495 - 501
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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