Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T13:16:41.886Z Has data issue: false hasContentIssue false
  • English
  • Français

The t3, moves conjecture for oriented links with matched diagrams

Published online by Cambridge University Press:  24 October 2008

Józef H. Przytycki
Józef H. Przytycki
Affiliation:
Mathematics Department, University of British Columbia, 121-1984 Mathematics Road, Vancouver, CanadaV6T 1Y4 and Warsaw University, Poland
Get access Rights & Permissions [Opens in a new window]

Extract

The local change in an oriented link diagram which replaces by k positive half-twists is called a tk move. For k even, the local change replacing by is called a tk move. For an unoriented diagram define a k-move, replacing by for any k. The following conjecture was stated in [14] and [10].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 1 , July 1990 , pp. 55 - 61
Copyright
Copyright © Cambridge Philosophical Society 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Anstee, R. P., Przytycki, J. H. and Rolfsen, D.. Knot polynomials and generalized mutation. Topology and its Appl. 32 (3) (1989), 237–249.CrossRefGoogle Scholar
[2]Bonahon, F. and Siebenmann, L.. Geometric Splittings of Classical Knots and the Algebraic Knots of Conway. London Math. Soc. Lecture Note Ser. no. 75. (To appear.)Google Scholar
[3]Burde, G. and Zieschang, H.. Knots. De Gruyter Studies in Math. no. 5. (De Gruyter, 1985).Google Scholar
[4]Caudron, A.. Classification des noeudes et des enlacements. Prepublications Université Paris-Sud (1981).Google Scholar
[5]Conway, J. H.. An enumeration of knots and links, and some of their algebraic properties. In Computational Problems in Abstract Algebra (editor Leech, J.) (Pergamon, 1969), pp. 329–358.Google Scholar
[6]Freyd, P., Yetter, D., Hoste, J., Lickorish, W. B. R., Millett, K. and Ocneanu, A.. A new polynomial invariant of knots and links. Bull. Amer. Math. Soc. 12 (1985), 239–246.CrossRefGoogle Scholar
[7]Jaeger, F.. On Tutte polynomials and link polynomials. Proc. Amer. Math. Soc. 103 (1988), 647–654.CrossRefGoogle Scholar
[8]Jones, V. F. R.. Hecke algebra representations of braid groups and link polynomials. Ann. of Math. (2) 126 (1987), 335–388.CrossRefGoogle Scholar
[9]Lickorish, W. B. R. and Millett, K. C.. Some evaluations of link polynomials. Comment. Math. Helv. 61 (1986), 349–359.CrossRefGoogle Scholar
[10]Morton, H. R.. Problems. In Braids (editors Birman, J. S., Libgober, A.). Contemp. Math. no. 78 (American Mathematical Society, 1988), pp. 557–574.CrossRefGoogle Scholar
[11]Murakami, H.. Unknotting number and polynomial invariants of a link. (Preprint, 1985.)Google Scholar
[12]Murakami, H.. On the derivatives of the Jones polynomial. Kobe J. Math. 3 (1986), 61–64.Google Scholar
[13]Przytycka, T. and Przytycki, J. H.. Invariants of chromatic graphs. Technical Report 88–22, University of British Columbia (1988).Google Scholar
[14]Przytycki, J. H.. t k moves on links. In Braids (editors Birman, J. S., Libgober, A.). Contemp. Math. no. 78 (American Mathematical Society, 1988), pp. 615–656.CrossRefGoogle Scholar
[15]Przytycki, J. H.. Elementary conjectures in classical knot theory. (To appear.)Google Scholar
[16]Przytycki, J. H. and Traczyk, P.. Invariants of links of Conway type. Kobe J. Math. 4 (1987), 115–139.Google Scholar
[17]Rolfsen, D.. Knots and Links. Math. Lecture Ser. no. 7 (Publish or Perish, 1976).Google Scholar
[18]Traldi, L.. A dichromatic polynomial for weighted graphs and link polynomials. Proc. Amer. Math. Soc. 106 (1989), 279–286.CrossRefGoogle Scholar