Indice des sous facteurs, algèbres de Hecke et théorie des noeuds

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1. [1] J.W. Alexander - A lemma on systems of knotted curves, Proc. Nat. Acad.9(1923), p. 93-95. JFM49.0408.03
2. [2] J.W. Alexander - Topological invariants of knots and links, Trans. Amer. Math. Soc.30(1928), p. 275-306. Zbl54.0603.03MR1501429JFM54.0603.03
3. [3] E. Artin - Theorie der Zopfe, Hamburg, Abh 9, p. 47-72. Zbl51.0450.01JFM51.0450.01
4. [4] R.J. Baxter - Exactly solved models in statistical mechanics, Acad. Press, London (1982). Zbl0723.60120MR690578
5. [5] D. Bennequin - Entrelacements et structures de contact, Thèse, Paris (1982). 
6. [6] J. Birman - Braids, links and mapping class groups, Ann. Math. Studies, 82(1974). Zbl0305.57013MR375281
7. [7] J. Birman - On the Jones polynomial of the closed 3 braids, (Preprint). MR799267
8. [8] N. Bourbaki - Groupes et Algèbres de Lie, Chap. 4, 5, 6, n° 1337, Hermann, Paris, 1960-1972. Zbl0483.22001
9. [9] O. Bratelli - Inductive limits of finite dimensional C* algebras, Trans. AMS171(1972), p. 195-234. Zbl0264.46057MR312282
10. [10] E. Brieskorn - Sur les groupes de tresses, Sém. Bourbaki n° 401, 1971-1972. Zbl0277.55003
11. [11] F. Bruhat et J. Tits - Groupes réductifs sur un corps local, Ch. 1, Publ. IHES, Vol. 41 (1972). Zbl0254.14017MR327923
12. [12] W. Burau - Über Zopfgruppen und gleichsinning verdrillte verkettunger, Abh. Math. Sem. Hanischen Univ.11(1936), p. 171-178. Zbl0011.17704
13. [13] J.H. Conway - An enumeration of knots and links, computational problems inAbstract Algebra, Pergamon, N.Y. (1970), p. 329-358. Zbl0202.54703MR258014
14. [14] J. Dixmier - Les algèbres d'opérateurs dans l'espace Hilbertien, Deuxième édition, Gauthier Villars (1969). Zbl0088.32304
15. [15] P. Freyd, D. Yetter, J. Hoste, W.B.R. Lickorish, K. Millett and A. Ocneanu - A new polynomial invariant of knots and links, Bull. A.M.S., Vol. 12, n° 2 (April 1985). Zbl0572.57002MR776477
16. [16] P. Freyd and D. Yetter - A new invariant for knots and links, Preprint (Sept. 1985). 
17. [17] F. Garside - The braid group and other groups, Quart. J. Math., Oxford20 (1969), p. 235-254. Zbl0194.03303MR248801
18. [18] M. Goldman - On subfactors of type II1 - Mich. Math. J.7(1960), p. 167-172. Zbl0121.10002MR107827
19. [19] N. Iwahori and H. Matsumoto - On some Bruhat decomposition and the structure of the Hecke rings of p -adic Chevalley groups, Public. IHES, Vol. 25 (1965), p. 5-48. Zbl0228.20015MR185016
20. [20] V. Jones - L'indice des sous-facteurs de type II1, C.R. Ac. Sci. Paris, t. 286(1977), p. 597-598. Zbl0344.46128MR430803
21. [21] V. Jones - A polynomial invariant for knots via von Neumann Algebras, Bull. Amer. Math. Soc.12(1985), p. 103-112. Zbl0564.57006MR766964
22. [22] V. Jones - Groupes de tresses, algèbres de Hecke et facteurs de type II1, C.R. Ac. Sci. Paris, t. 298, Sér. I, n° 20 (1984). Zbl0597.20034MR753900
23. [23] V. Jones - Index for subfactors, Invent. Math.72(1983), p. 1-25. Zbl0508.46040MR696688
24. [24] V. Jones - Braid groups, Hecke algebras and type II1 factors, Proc. Japan-US Conf. (1983), (Preprint). Zbl0659.46054
25. [25] V. Jones - Sur la conjugaison des sous-facteurs des facteurs de type II1, C.R. Ac. Sc. Paris, t. 286(1977), p. 597-598. Zbl0344.46128MR430803
26. [26] L.H. Kauffman - A geometric interpretation of the generalized polynomial, Preprint (1985). 
27. [27] D. Kazhdan and G. Lusztig - Representations of Coxeter groups and Hecke algebras, Invent. Math.53(1979), p. 165-184. Zbl0499.20035MR560412
28. [28] D. Kazhdan and G. Lusztig - Schubert varieties and Poinearé duality, Proc. Symp. Pure Math., Vol. 36(1980). Zbl0461.14015MR573434
29. [29] H. Kosaki - Extension of Jones' theory of index to arbitrary factors, Preprint MSRI, Berkeley, 1985. MR829381
30. [30] J. Lannes - Sur l'invariant de Kervaire pour les noeuds classiques, Preprint, Ecole Polytechnique (1984). MR767901
31. [31] W.B.R. Lickorish and K.C. Millett - A polynomial invariant of oriented links, Preprint (January 1985). MR880512
32. [32] W.B.R. Lickorish - Prime knots and tangles, Trans. Amer. Math. Soc.267(1981). Zbl0472.57004MR621991
33. [33] H.N.V. Tempercey and E.H. Lieb - Proc. Royal Soc., London, (1971), p. 251-280. Zbl0211.56703
34. [34] A.A. Markov - Über die freie Aequivalenz geschlossener zopfe, Mat. Sb1 (1935), p. 73-78. JFM62.0658.01
35. [35] H. Matsumoto - Analyse harmonique dans les systèmes de Tits bornologiques de type affine, Lecture Notes in Math., Springer, Vol. 590(1977). Zbl0366.22001MR579177
36. [36] H.R. Morton - The Jones polynomial for unoriented links, Preprint, University of Liverpool (1985). Zbl0595.57006MR830630
37. [37] H.R. Morton - Threading knot diagrams, Preprint, University of Liverpool. Zbl0595.57007MR817666
38. [38] H.R. Morton - Closed braids representatives for a link and its Jones-Conway polynomial, Preprint (1985). 
39. [39] K. Murasugi - Jones polynomials of special alternating knots, (Preprint). 
40. [40] F. Murray and J. von Neumann - On rings of operators II, Trans. A.M.S.41 (1937), p. 208-248. Zbl0017.36001MR1501899
41. [41] F. Murray and J. von Neumann - On rings of operators IV, Ann. Math.44(1943), p. 716-808. Zbl0060.26903MR9096
42. [42] A. Ocneanu - A polynomial invariant for knots. A combinatorial and an algebraic approach, Preprint MSRI (1984). 
43. [43] M. Pimsner and S. Popa - Entropy and index for subfactors, Preprint INCREST, Bucharest (1983). MR860811
44. [44] J.H. Przytycki and P. Traczyk - Invariants of links of Conway type, Preprint, (1985). MR945888
45. [45] B. Seifert - The spherical traces for Hecke algebras associated to type II1 factors, Preprint IHES (1985). 
46. [46] M. Takesaki - Theory of operator algebras I, Berlin, Heidelberg, New York, Springer (1979). Zbl0436.46043MR548728
47. [47] H. Umegaki - Conditional expectation in an operator algebra I, Tohoku Math. J.6, (1954), p. 358-362. Zbl0057.09702MR68751
48. [48] J. Van Buskirk - A version of the generalized Jones polynomial which is positive for positive knots, Preprint, University of Oregon (1985). MR823288
49. [49] A. Wassermann - Automorphic actions of compact groups, Thesis, University of Pennsylvania (1981). 
50. [50] H. Wenzl - On sequences of projections, Preprint, University of Pennsylvania (1984). MR873400

1. Pierre Cartier, Développements récents sur les groupes de tresses. Applications à la topologie et à l'algèbre