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Strongly plus-amphicheiral knots are algebraically slice

Published online by Cambridge University Press:  24 October 2008

D. D. Long
Affiliation:
St John's College, Cambridge†

Extract

A classical knot in S3 is said to be slice if it is the boundary of a smooth (or PL locally unknotted) disc in B4. The first obstructions to sliceness were introduced in [3] (the Alexander polynomial is of the form f(t). f(t−1)) and [7] (the signature is zero). Levine defined the notion of algebraically slice knot in [5]. This property implies the first two obstructions vanish.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Conway, J. H.. An enumeration of knots and links. In Computational Problems in Abstract Algebra (Pergamon Press, 1969), pp. 329358.Google Scholar
[2]Hartley, R. and Kawauchi, A.. Polynomials of amphicheiral knots. Math. Ann. 243 (1979), 6370.CrossRefGoogle Scholar
[3]Fox, R. H. and Milnor, J. W.. Singularities of 2-spheres in 4-space and cobordism of knots. Osaka J. Math. 3 (1966), 257267.Google Scholar
[4]Livingston, C.. Knots which are not concordant to their reverse. (Preprint.)Google Scholar
[5]Levine, J.. Knot cobordism groups in codimension two. Comment. Math. Helv. 44 (1969), 229244.CrossRefGoogle Scholar
[6]Milnor, J. W.. Infinite cyclic coverings. In Conference on the Topology of Manifolds (Prindle, Weber and Schmidt, 1968), pp. 115133.Google Scholar
[7]Murasugi, K.. On a certain numerical invariant of link types. Trans. Amer. Math. Soc. 117 (1965), 387422.CrossRefGoogle Scholar