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On the 2-Parallel Versions of Links

Published online by Cambridge University Press:  20 November 2018

Jae-Ho Chang ,
Sang Youl Lee  and
Chan-Young Park
Jae-Ho Chang
Affiliation:
Department of Mathematics Dongguk University Kyongju 780-714 Korea, e-mail: [email protected]
Sang Youl Lee
Affiliation:
Department of Mathematics Pusan National University Pusan 609-735 Korea, e-mail: [email protected]
Chan-Young Park
Affiliation:
Department of Mathematics College of Natural Sciences Kyungpook National University Taegu 702-701 Korea, e-mail: [email protected]
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Abstract

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In this paper, we show that the absolute value of the signature of the 2-parallel version of a link is less than or equal to the nullity of it and show that the signature, nullity, and Minkowski units of the 2-parallel version of a certain class of links are always equal to 0, 2, and 1 respectively.

Keywords

57M25braidGoeritz matrixMinkowski unitnullitysignature2-parallel version
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 2 , 01 June 2000 , pp. 145 - 156
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Birman, J. S., Braids, Links, and Mapping Class Groups. Ann. of Math. Stud. 82, Princeton University Press, 1974.Google Scholar
[2] Goeritz, L., Knoten und quadratische Formen. Math. Z. 36(1933), 647–654.Google Scholar
[3] Gordon, C. McA. and Litherland, R. A., On the signature of a link. Invent.Math. 47(1978), 53–69.Google Scholar
[4] Gordon, C. McA., Litherland, R. A. and Murasugi, K., Signatures of covering links. Canad. Math, J.. 33(1981), 381–394.Google Scholar
[5] Jones, B. W., The arithmetic theory of quadratic forms. Carus Math. Monographs 10, John Wiley and Sons, 1950.Google Scholar
[6] Kyle, R. H., Branched covering spaces and the quadratic forms of links. Ann. of Math. (2) 59(1954), 539–548.Google Scholar
[7] Lee, Sang Youl, On the Minkowski units of 2-periodic knots. Submitted.Google Scholar
[8] Murakami, J., The parallel version of polynomial invariants of links. Osaka Math, J.. 26(1989), 1–55.Google Scholar
[9] Murasugi, K., On a certain numerical invariant of link types. Trans. Amer.Math. Soc. 117(1965), 387–422.Google Scholar
[10] Murasugi, K., On the Minkowski unit of slice links. Trans. Amer.Math. Soc. 114(1965), 377–383.Google Scholar
[11] Traldi, L., On the Goeritz Matrix of a link. Math. Z. 188(1985), 203–213.Google Scholar