Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-26T15:04:54.396Z Has data issue: false hasContentIssue false

On adequate links and homogeneous links

Published online by Cambridge University Press:  17 April 2009

Sang Youl Lee
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609–735, Korea e-mail: sangyoul@hyowon.pusan.ac.kr
Chan-Young Park
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702–701, Korea e-mail: chnypark@knu.ac.kr
Myoungsoo Seo
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702–701, Korea e-mail: myseo@kebi.com
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.

In this paper, we give several inequalities concerning the genus and the degree of the Jones Polynomial of an adequate link and of a homogeneous link and their applications.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Bennequin, D., ‘Entrelacements et équations de Pfaff’, Astérisque 107108 (1983), 87161.Google Scholar
[2]Cromwell, P.R., ‘Homogeneous links’, J. London Math. Soc. 39 (1989), 535552.CrossRefGoogle Scholar
[3]Kauffman, L.H., Formal knot theory, Mathematical Notes 30 (Princeton University Press, Princeton, 1983).Google Scholar
[4]Kauffman, L.H., ‘State models and the Jones polynomial’, Topology 26 (1987), 395407.Google Scholar
[5]Kauffman, L.H., ‘New invariants in the theory of knots’, Amer. Math. Monthly 3 (1988), 195242.CrossRefGoogle Scholar
[6]Lickorish, W.B.R., An introduction to knot theory, Graduate texts in Mathematics 175 (Springer Verlag, New York, 1997).CrossRefGoogle Scholar
[7]Lickorish, W.B.R. and Thistlethwaite, M.B., ‘Some links with non-trivial polynomials and their crossing-numbers’, Comment. Math. Helv. 63 (1988), 527539.Google Scholar
[8]Menasco, W.W. and Thistlethwaite, M.B., ‘The classification of alternating links’, Ann. of Math. 138 (1993), 113171.Google Scholar
[9]Morton, H.R., ‘Seifert circles and knot polynomials’, Math. Proc. Cambridge Philos. Soc. 99 (1986), 107109.Google Scholar
[10]Murasugi, K., ‘On a certain numerical invariant of link types’, Trans. Amer. Math. Soc. 117 (1965), 387422.CrossRefGoogle Scholar
[11]Murasugi, K., ‘Jones polynomials and classical conjectures in knot theory’, Topology 26 (1987), 187194.CrossRefGoogle Scholar
[12]Murasugi, K., ‘Jones polynomials and classical conjectures in knot theory. II’, Math. Proc. Cambridge Philops. Soc. 102 (1987), 317318.CrossRefGoogle Scholar
[13]Murasugi, K., ‘On invariants of graphs with applications to knot theory’, Trans. Amer. Math. Soc. 314 (1989), 149.CrossRefGoogle Scholar
[14]Nakamura, T., ‘Positive alternating links are positively alternating’, J. Knot Theory Ramifications 9 (2000), 107112.CrossRefGoogle Scholar
[15]Rolfsen, D., Knots and links, Mathematics Lecture Series 7 (Publish or Perish Inc., Houston, TX, 1976).Google Scholar
[16]Seifert, H., ‘Uber das Geschlecht von Knoten’, Math. Ann. 110 (1935), 571592.Google Scholar
[17]Stoimenow, A., ‘Positive knots, closed braids and the Jones polynomial’, (preprint 1998).Google Scholar
[18]Stoimenow, A., ‘On some restrictions to the values of the Jones polynomial’, (preprint 1999).Google Scholar
[19]Thistlethewaite, M.B., ‘A spanning tree expansion of the Jones polynomial’, Topology 26 (1987), 297309.Google Scholar
[20]Thistlethewaite, M.B., ‘On the Kauffman polynomial of an adequate link’, Invent. Math. 93 (1988), 285296.CrossRefGoogle Scholar