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On adequate links and homogeneous links

Published online by Cambridge University Press:  17 April 2009

Sang Youl Lee ,
Chan-Young Park  and
Myoungsoo Seo
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, Kyungpook National University, Taegu 702–701, Korea e-mail: [email protected]
Myoungsoo Seo
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702–701, Korea e-mail: [email protected]
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Abstract

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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
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 395 - 404
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Bennequin, D., ‘Entrelacements et équations de Pfaff’, Astérisque 107–108 (1983), 87–161.Google Scholar
[2]Cromwell, P.R., ‘Homogeneous links’, J. London Math. Soc. 39 (1989), 535–552.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), 395–407.Google Scholar
[5]Kauffman, L.H., ‘New invariants in the theory of knots’, Amer. Math. Monthly 3 (1988), 195–242.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), 527–539.Google Scholar
[8]Menasco, W.W. and Thistlethwaite, M.B., ‘The classification of alternating links’, Ann. of Math. 138 (1993), 113–171.Google Scholar
[9]Morton, H.R., ‘Seifert circles and knot polynomials’, Math. Proc. Cambridge Philos. Soc. 99 (1986), 107–109.Google Scholar
[10]Murasugi, K., ‘On a certain numerical invariant of link types’, Trans. Amer. Math. Soc. 117 (1965), 387–422.CrossRefGoogle Scholar
[11]Murasugi, K., ‘Jones polynomials and classical conjectures in knot theory’, Topology 26 (1987), 187–194.CrossRefGoogle Scholar
[12]Murasugi, K., ‘Jones polynomials and classical conjectures in knot theory. II’, Math. Proc. Cambridge Philops. Soc. 102 (1987), 317–318.CrossRefGoogle Scholar
[13]Murasugi, K., ‘On invariants of graphs with applications to knot theory’, Trans. Amer. Math. Soc. 314 (1989), 1–49.CrossRefGoogle Scholar
[14]Nakamura, T., ‘Positive alternating links are positively alternating’, J. Knot Theory Ramifications 9 (2000), 107–112.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), 571–592.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), 297–309.Google Scholar
[20]Thistlethewaite, M.B., ‘On the Kauffman polynomial of an adequate link’, Invent. Math. 93 (1988), 285–296.CrossRefGoogle Scholar