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Fox's congruence classes and the quantum-SU(2) invariants of links in 3-manifolds

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Commentarii Mathematici Helvetici

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References

  1. P. M. Cohn,Algebra (2nd edition) Volume 2. John Wiley and Sons, 1989.

  2. R. H. Fox,Congruence classes of knots. Osaka Math. J.10 (1958) 37–41.

    MathSciNet  Google Scholar 

  3. R. Kirby,The topology of 4-manifolds. Lecture Notes in Math.1374, Springer, 1989.

  4. R. Kirby andP. Melvin, The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, ℂ). Invent. Math.105 (1991) 473–545.

    Article  MathSciNet  Google Scholar 

  5. W. B. R. Lickorish,A representation of orientable combinatorial 3-manifolds, Ann. of Math.76 (1962) 531–540.

    Article  MathSciNet  Google Scholar 

  6. W. B. R. Lickorish,Calculations with the Temperley-Lieb algebra. Comment. Math. Helvetici67 (1992) 571–591.

    Article  MathSciNet  Google Scholar 

  7. W. B. R. Lickorish,The skein method for three-manifold invariants. J. Knot Theory and its Ramifications2 (1993) 171–194.

    Article  MathSciNet  Google Scholar 

  8. W. B. R. Lickorish andM. B. Thistlethwaite,Some links with non-trivial polynomials and their crossing-numbers. Comment. Math. Helvetici63 (1988) 527–539.

    Article  MathSciNet  Google Scholar 

  9. Y. Nakanishi,On Fox's congruence classes of knots, II. Osaka J. Math.27 (1990) 207–215.

    MathSciNet  Google Scholar 

  10. Y. Nakanishi andS. Suzuki,On Fox's congruence classes of knots. Osaka J. Math.24 (1987) 217–225.

    MathSciNet  Google Scholar 

  11. N. Y. Reshetikhin andV. G. Turaev,Invariants of 3-manifolds via link polynomials and quantum groups. Invent Math.1035 (1991) 547–597.

    Article  MathSciNet  Google Scholar 

  12. J. D. Roberts,Skein theory and Turaev-Viro invariants. Topology34 (1995) 771–787.

    Article  MathSciNet  Google Scholar 

  13. D. Rolfsen,Knots and links. Publish or Perish, 1976.

  14. V. G. Turaev,State sum models in low-dimensional topology. Proc. ICM, Kyoto, Japan, 1990 (Math. Soc. Japan, Springer-Verlag 1991) 689–698.

  15. E. Witten,Quantum field theory and Jone's polynomial. Comm. Math. Phys.121 (1989) 351–399.

    Article  MathSciNet  Google Scholar 

  16. S. Yamada,A topological invariant of spatial regular graphs, ‘Knots 90’ (ed. A. Kawauchi), de Gruyter 1992, 447–454.

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Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, England

    Marc Lackenby

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  1. Marc Lackenby
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Lackenby, M. Fox's congruence classes and the quantum-SU(2) invariants of links in 3-manifolds. Commentarii Mathematici Helvetici 71, 664–677 (1996). https://doi.org/10.1007/BF02566441

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