The universal Vassiliev-Kontsevich invariant for framed oriented links

Tu Quoc Thang Le; Jun Murakami

Compositio Mathematica (1996)

  • Volume: 102, Issue: 1, page 41-64
  • ISSN: 0010-437X

How to cite


Le, Tu Quoc Thang, and Murakami, Jun. "The universal Vassiliev-Kontsevich invariant for framed oriented links." Compositio Mathematica 102.1 (1996): 41-64. <>.

author = {Le, Tu Quoc Thang, Murakami, Jun},
journal = {Compositio Mathematica},
keywords = {Reshetikhin-Turaev functor; tangles; Kontsevich integral; framed oriented links; Vassiliev-Kontsevich invariant},
language = {eng},
number = {1},
pages = {41-64},
publisher = {Kluwer Academic Publishers},
title = {The universal Vassiliev-Kontsevich invariant for framed oriented links},
url = {},
volume = {102},
year = {1996},

AU - Le, Tu Quoc Thang
AU - Murakami, Jun
TI - The universal Vassiliev-Kontsevich invariant for framed oriented links
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 102
IS - 1
SP - 41
EP - 64
LA - eng
KW - Reshetikhin-Turaev functor; tangles; Kontsevich integral; framed oriented links; Vassiliev-Kontsevich invariant
UR -
ER -


  1. [Al-Co] Altschuler, D. and Coste, A.: Quasi-quantum groups, knots, three-manifolds, and topological field theoryCommun. Math. Phys.150 (1992) pp. 83-107. Zbl0773.57004MR1188498
  2. [Ar] Arnold, V.: Talk at ECM, Paris1990. 
  3. [Baez] Baez, J.C.: Link invariants of finite type and perturbation theory, Wellesley college preprint, 1992. Zbl0792.57002MR1193625
  4. [Bar1] Bar-Natan, Dror: On the Vassiliev knot invariants, Harvard University preprint, August 1992. MR1318886
  5. [Bar2] Bar-Natan, Dror: Vassiliev invariants of homotopy string links, Harvard University preprint, 1993. 
  6. [Bir] Birman, J.S.: New points of view in knot theoryBull. Amer. Math. Soc.28 (1993) No 2, 253-287. 225-270. Zbl0785.57001MR1191478
  7. [Bir2] Birman, J.: Braids, links, and mapping class groups, Princeton University Press, 1974. Zbl0305.57013MR375281
  8. [Bir-Lin] Birman, J.S. and Lin, X.S.: Knot polynomials and Vassiliev's invariants, Invent. Math.111 (1993) pp. 225-270. Zbl0812.57011MR1198809
  9. [Car] Cartier, P.: Construction combinatoire des invariants de Vassiliev-Kontsevich des nœuds, C. R. Acad. Sci. Paris, t. 316 (1993) series 1, pp. 1205-1210F. Zbl0791.57006
  10. [Drin1] Drinfel'd, V.G.: On Quasi-Hopf algebrasLeningrad Math. J.1 (1990) 1419-1457. Zbl0718.16033MR1047964
  11. [Drin2] Drinfel'd, V.G.: On quasi-triangular quasi-Hopf algebras and a group closely connected with Gal(Q/Q)Leningrad Math. J.2 (1990) 829-860. Zbl0728.16021MR1080203
  12. [Drin3] Drinfel'd, V.G.: Quantum groups, Proceeding of the ICM, Berkerley, 1986, 798-820. Zbl0667.16003MR934283
  13. [F-dV] Freudenthal, H.: de Vries, Linear Lie Groups, Academic Press, New YorkLondonTorontoSydneySan Francisco, 1969. Zbl0377.22001MR260926
  14. [Jim] Jimbo, M.: A q-difference analogue of U(g) and the Yang-Baxter equation. Lett. Math. Phys.10 (1985) 63-69. Zbl0587.17004MR797001
  15. [Kas] Kassel, C.: Quantum groups, to appear in the series Graduate Texts in Mathematics, Springer-Verlag, in 1994. Zbl0808.17003MR1321145
  16. [Kauff] Kauffman, L.: Vassiliev invariants and the loop states in quantum gravity, University of Illinois at Chicago preprint 1993, to appear in Knots and quantum gravity, Oxford U. Press. Zbl0884.57009MR1309915
  17. [Koh] Kohno, T.: Monodromy representations of braid groups and Yang-Baxter equations, Ann. Inst. Fourier, 37 (1987) 139-160. Zbl0634.58040MR927394
  18. [Kont1] Kontsevich, M.: Vassiliev's knot invariants, Adv. Sov. Math., 16, part 2, (1993) 137-150. Zbl0839.57006MR1237836
  19. [Kont2] Kontsevich, M.: Talk at ECM, Paris1990. 
  20. [Le-Mu1] Le, T.Q.T. and Murakami, J.: Kontsevich's integral for Homfly polynomial and relation between values of multiple zeta functions, Max-Planck Institut für Mathematik preprint MPI/93-26, Bonn1993. 
  21. [Le-Mu2] Le, T.Q.T. and Murakami, J.: Kontsevich's integral for Kauffman polynomial, Max-Planck Institut für Mathematik preprint , Bonn1993. 
  22. [Le-Mu3] Le, T.Q.T. and Murakami, J.: Representation of the Category of Tangles by Kontsevich's iterated integral, Max-Planck Institut für Mathematik preprint, Bonn1993. 
  23. [Lin] Lin, X.S.: Vertex models, quantum groups and Vassiliev's knot invariants, Columbia University, preprint 1992. Zbl1179.57021
  24. [Piu1] Piunikhin, S.: Combinatorial expression for universal Vassiliev link invariant, Harvard University preprint, 1993. Zbl0828.57007MR1264316
  25. [Piu2] Piunikhin, S.: Weights of Feynman diagrams, link polynomials and Vassilev knot invariants, MoscowState University preprint, 1992. 
  26. [Re-Tu] Reshetikhin, N. Yu. and Turaev, V.G.: Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys., 127 (1990) pp. 262-288. Zbl0768.57003MR1036112
  27. [So] Sossinsky, A.B.: Feynman diagrams and Vassiliev invariants, IHES preprint IHES/M/92/13,1992. 
  28. [St] Stanford, T.: Finite type invariants of knots, links, and graphs, Columbia University preprint, 1992. MR1404922
  29. [Tu1] Turaev, V.G.: Operator invariants of tangles and R-matrices, Math. USSR Izvestija35 (1990) pp. 411-444. Zbl0707.57003MR1024455
  30. [Tu2] Turaev, V.G.: The Yang-Baxter equations and invariants of links, Invent. Math.92 (1988) pp. 527-553. Zbl0648.57003MR939474
  31. [Va] Vassiliev, V.: Cohomology of knot spaces, Theory of singularities and its applications (Providence (Arnold, V. I. ed.), Amer. Math. Soc., Providence, 1990. MR1089670
  32. [Za] Zagier, D.: Values of multiple zeta functions and applications, MPI für Mathematik, preprint, Bonn1993, to appear in Proceeding of ECM. MR1296720

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