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The Higher homotopy groups of the p-spun trefoil knot

Published online by Cambridge University Press:  18 May 2009

W. A. McCallum
W. A. McCallum
Affiliation:
Kansas State University
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In this paper we show that the (p+l)st homotopy group of the p-spun trefoil knot is nontrivial. This result was obtained for p = 1 in [1] using duality arguments. Here we take a totally different approach via the algorithm given in [3] and a module representation giving a simpler and more natural argument.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 1 , January 1976 , pp. 44 - 46
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

REFERENCES

1.Andrews, J. J. and Curtis, M. L., Knotted 2-spheres in the 4-sphere, Ann. Math. 70 (1959), 565–571.CrossRefGoogle Scholar
2.Fox, R. H., On the Complementary Domains of a Pair of Inequivalent Knots, Indag Math. 14 (1952), No. 1, 37–40.CrossRefGoogle Scholar
3.McCallum, W. A., The Higher Homotopy Groups of Links, Diff. Geo. (to appear).Google Scholar
4.Sumners, D. W., On an Unlinking Theorem, Proc. Cambridge Philos. Soc. Math. Phy. Sci. 71 (1972), 1–4.CrossRefGoogle Scholar