A recursive calculation of the Arf invariant of a link

Hitoshi MURAKAMI

doi:10.2969/jmsj/03820335

Hitoshi MURAKAMI

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 2 Pages 335-338

DOI https://doi.org/10.2969/jmsj/03820335

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Published: 1986 Received: November 22, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. H. Conway, An enumeration of knots and links, and some of their algebraic properties, Computational Problems in Abstract Algebra, Pergamon Press, Oxford and New York, 1969, 329-358.
2) C. McA. Gordon (ed.), Problems, Knot Theory (Proc., Plans-sur-Bex, 1977), Lecture Notes in Math., 685, Springer-Verlag, 1978, 309-311.
3) J. Hoste, The Arf invariant of a totally proper link, Topology Appl., 18(1984), 163-177.
4) J. Hoste, A polynomial invariant of knots and links, preprint, Rutgers Univ., 1984.
5) V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc., 12 (1985), 103-111.
6) L. H. Kauffman, The Conway polynomial, Topology, 20(1981), 101-108.
7) L. H. Kauffman, Formal Knot Theory, Math. Notes, 30, Princeton Univ. Press, 1983.
8) W. B. R. Lickorish and K. C. Millett, Topological invariants of knots and links, preprint, 1984.
9) H. Murakami, The Arf invariant and the Conway polynomial of a link, Math. Sem. Notes Kobe Univ., 11(1983), 335-344.
10) K. Murasugi, On the Arf invariant of links, Math. Proc. Cambridge Philos. Soc., 95 (1984), 61-69.
11) R. A. Robertello, An invariant of knot cobordism, Comm. Pure Appl. Math., 18 (1965), 543-555.
12) Y. Matsumoto, An elementary proof of Rochlin's signature theorem and its extension by Guillou and Marin, preprint, 1977, (to appear in Astérisque).

Right : [1] J. H. Conway, An enumeration of knots and links, and some of their algebraic properties, Computational Problems in Abstract Algebra, Pergamon Press, Oxford and New York, 1969, 329-358.
[2] C. McA. Gordon (ed.), Problems, Knot Theory (Proc., Plans-sur-Bex, 1977), Lecture Notes in Math., 685, Springer-Verlag, 1978, 309-311.
[3] J. Hoste, The Arf invariant of a totally proper link, Topology Appl., 18(1984), 163-177.
[4] J. Hoste, A polynomial invariant of knots and links, preprint, Rutgers Univ., 1984.
[5] V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc., 12 (1985), 103-111.
[6] L. H. Kauffman, The Conway polynomial, Topology, 20(1981), 101-108.
[7] L. H. Kauffman, Formal Knot Theory, Math. Notes, 30, Princeton Univ. Press, 1983.
[8] W. B. R. Lickorish and K. C. Millett, Topological invariants of knots and links, preprint, 1984.
[9] H. Murakami, The Arf invariant and the Conway polynomial of a link, Math. Sem. Notes Kobe Univ., 11(1983), 335-344.
[10] K. Murasugi, On the Arf invariant of links, Math. Proc. Cambridge Philos. Soc., 95 (1984), 61-69.
[11] R. A. Robertello, An invariant of knot cobordism, Comm. Pure Appl. Math., 18 (1965), 543-555.
[12] Y. Matsumoto, An elementary proof of Rochlin's signature theorem and its extension by Guillou and Marin, preprint, 1977, (to appear in Astérisque).

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