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Jones and polynomials for -bridge knots and links
Author:
Taizo Kanenobu
Journal:
Proc. Amer. Math. Soc. 110 (1990), 835-841
MSC:
Primary 57M25
MathSciNet review:
1025279
Full-text PDF Free Access
Abstract |
References |
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Additional Information
Abstract: It is known that the polynomial of a -bridge knot or link can be obtained from the Jones polynomial. We construct arbitrarily many -bridge knots or links with the same polynomial but distinct Jones polynomials.
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- [1]
- R. D. Brandt, W. B. R. Lickorish, and K. C. Millett, A polynomial invariant for unoriented knots and links, Invent. Math. 84 (1986), 563-573. MR 837528 (87m:57003)
- [2]
- G. Burde and H. Zieschang, Knots, De Gruyter Studies in Math., vol. 5, Walter de Gruyter, Berlin and New York, 1985. MR 808776 (87b:57004)
- [3]
- J. H. Conway, An enumeration of knots and links, in Computational Problems in Abstract Algebra (J. Leech, ed.), Pergamon Press 1969, 329-358. MR 0258014 (41:2661)
- [4]
- C. F. Ho, A new polynomial invariant for knots and links--preliminary report, Abstracts Amer. Math. Soc. 6 (1985), 300.
- [5]
- V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985), 103-111. MR 766964 (86e:57006)
- [6]
- T. Kanenobu, Examples on polynomial invariants of knots and links, Math. Ann. 275 (1986), 555-572. MR 859330 (88b:57010)
- [7]
- -, Relations between the Jones and Q polynomials for
-bridge and -braid links, Math. Ann. 285 (1989), 115-124. MR 1010195 (90i:57002)
- [8]
- -, Examples on polynomial invariants of knots and links II, Osaka J. Math. 26 (1989), 465-482. MR 1021426 (91e:57018)
- [9]
- T. Kanenobu and T. Sumi, in preparation.
- [10]
- L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), 395-407. MR 899057 (88f:57006)
- [11]
- M. E. Kidwell, On the degree of the Brandt-Lickorish-Millet-Ho polynomial of a link, Proc. Amer. Math. Soc. 100 (1987), 755-762. MR 894450 (89b:57003)
- [12]
- W. B. R. Lickorish and K. C. Miliett, A polynomial invariant of oriented links, Topology 26 (1987), 107-141. MR 880512 (88b:57012)
- [13]
- T. Miyauchi, On the highest degree of absolute polynomials of alternating links, Proc. Japan Acad. Ser. A 63 (1987), 174-177. MR 906987 (89b:57004)
- [14]
- K. Murasugi, Jones polynomials of alternating links, Trans. Amer. Math. Soc. 295 (1986), 147-174. MR 831194 (88f:57011)
- [15]
- D. Rolfsen, Knots and links, Math. Lecture Series no. 7, Publish or Perish, Berkeley, 1976. MR 0515288 (58:24236)
- [16]
- M. B. Thistlethwaite, A spanning tree expansion of the Jones polynomial, Topology 26 (1987), 297-309. MR 899051 (88h:57007)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-1025279-0
PII:
S 0002-9939(1990)1025279-0
Keywords:
-bridge knot,
-bridge link,
polynomial,
Jones polynomial
Article copyright:
© Copyright 1990 American Mathematical Society
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