Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T19:52:20.026Z Has data issue: false hasContentIssue false
  • English
  • Français

Alexander polynomials of two-bridge knots

Part of: Low-dimensional topology

Published online by Cambridge University Press:  09 April 2009

Yasutaka Nakanishi  and
Masaki Suketa
Yasutaka Nakanishi
Affiliation:
Department of MathematicsKobe UniversityNada-kuKobe 657Japan e-mail: [email protected]
Masaki Suketa
Affiliation:
Department of MathematicsKobe UniversityNada-kuKobe 657Japan e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For two-bridge knots, the authors give necessary conditions on coefficients of Alexander polynomials.

Keywords

Two-bridge knotAlexander polynomialSeifert matrix.

MSC classification

Secondary: 57M25: Knots and links in $S^3$
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 3 , June 1996 , pp. 334 - 342
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Burde, G., ‘Das Alexanderpolynom der Knoten mit zwei Brücken’, Arch. Math. 44 (1985), 180–189.CrossRefGoogle Scholar
[2]Burde, G., ‘Faserbare Knoten mit zwei Brücken’, preprint.Google Scholar
[3]Burde, G. and Zieschang, H., Knots (Gruyter, Berlin, 1985).Google Scholar
[4]Conway, J. H., ‘An enumeration of knots and links, and some of their algebraic properties’, in: Computational problems in abstract algebra (Pergamon Press, Oxford, 1969) pp. 329–358.Google Scholar
[5]Hartley, R. I., ‘On two-bridged knot polynomials’, J. Austral Math. Soc. (Ser. A) 28 (1979), 241–249.CrossRefGoogle Scholar
[6]Murasugi, K., ‘On the Alexander polynomial of the alternating knot’, Osaka J. Math. 10 (1958), 181–189.Google Scholar
[7]Rolfsen, D., Knots and links, Math. Lecture Series 7 (Publish or Perish Inc., Berkeley, 1976).Google Scholar
[8]Schubert, H., ‘Knoten mit zwei Brücken’, Math. Z. 65 (1956), 133–170.Google Scholar
[9]Seifert, H., ‘Über das Geschlecht von Knoten’, Math. Ann. 110 (1934), 571–592.Google Scholar