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On the Arf invariant of links

Published online by Cambridge University Press:  24 October 2008

Ying-Qing Wu
Ying-Qing Wu
Affiliation:
Mathematics Department, Peking University, Beijing, China
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Extract

In ([2], p. 310) the problem of relating the Arf invariant of a link to other link invariants, and finding practical ways of computing it, was raised. Murasugi gave a partial solution to this in [9]: if L has two components, then Arf(L), when defined, is given by

where l1, l2 are the components of L, and ΔL(t1, t2) denotes the Alexander polynomial of L.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 2 , September 1986 , pp. 355 - 359
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1] Hartley, R.. The Conway potential function for links. Comment. Math. Helv. 58 (1983), 365–378.CrossRefGoogle Scholar
[2] Hausmann, J. C.. (ed.) Knot Theory. Lecture Notes in Math. vol. 685 (Springer-Verlag, 1978).Google Scholar
[3] Hoste, J.. The Arf invariant of a totally proper link. Topology Appl. 18 (1984), 163–177.CrossRefGoogle Scholar
[4] Jones, V. F. R.. A polynomial invariant for knots via von Neumann algebras. Bull. Amer. Math. Soc. 12 (1985), 103–111.CrossRefGoogle Scholar
[5] Kauffman, L. H.. The Conway polynomial. Topology 20 (1980), 101–108.CrossRefGoogle Scholar
[6] Kauffman, L. H.. Formal Knot Theory. Math. Notes 30, Princeton University Press 1983.Google Scholar
[7] Murakami, H.. The Arf invariant and the Conway polynomial of a link. Math. Sem. Notes 11 (1983), 335–344.Google Scholar
[8] Murakami, H.. A recursive calculation of the Arf invariant of a link (to appear).Google Scholar
[9] Murasugi, K.. On the Arf invariant of links. Math. Proc. Cambridge Philos. Soc. 95 (1984), 61–69.CrossRefGoogle Scholar
[10] Robertello, R. A.. An invariant of knot cobordism. Comm. Pure Appl. Math. 18 (1965), 543–555.CrossRefGoogle Scholar