Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T14:32:51.670Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Gordon, C. McA.Problems in knot theory. Knot Theory Proceedings (Plans-sur-Bex). Lecture Notes in Mathematics, no. 685 (1978), 309–311.Google Scholar
(2)Kervaire, M.Les noeuds de dimension superieure. Butt. Soc. Math. France 93 (1965), 225–271.Google Scholar
(3)Kervaire, M.Knot cobordism in codimension two. Manifolds. Lecture Notes in Mathematics, no. 197 (1970), 83–105.Google Scholar
(4)Kirby, R. C. and Lickorish, W. B. R.Prime knots and concordance. Math. Proc. Cambridge Philos. Soc. 86 (1979), 437–441.CrossRefGoogle Scholar
(5)Levine, J. P.Knot cobordism groups in codimension two. Comment. Math. Helv. 44 (1969), 229–244.CrossRefGoogle Scholar
(6)Levine, J. P.An algebraic classification of some knots of codimension two. Comment. Math. Helv. 45 (1970), 185–198.CrossRefGoogle Scholar
(7)Serre, J.-P.Corps locaux (Hermann, 1968).Google Scholar
(8)Stoltzfus, N. W.Unraveling the integral knot concordance group. Mem. Amer. Math. Soc. 192 (1977).Google Scholar
(9)Trotter, H. F.Homology of group systems with applications to knot theory. Ann. Math. 76 (1962), 464–498.CrossRefGoogle Scholar
(10)Trotter, H. F.On S-equivalence of Seifert matrices. Invent. Math. 20 (1973), 173–207.CrossRefGoogle Scholar