A polynomial invariant for knots via von Neumann algebras
HTML articles powered by AMS MathViewer
- by Vaughan F. R. Jones PDF
- Bull. Amer. Math. Soc. 12 (1985), 103-111
References
-
1. J. W. Alexander, A lemma on systems of knotted curves, Proc. Nat. Acad. 9 (1923), 93-95.
- Rodney J. Baxter, Exactly solved models in statistical mechanics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1982. MR 690578 3. D. Bennequin, Entrelacements et structures de contact, These, Paris, 1982.
- Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281 5. W. Burau, Uber Zopfgruppen und gleichsinning verdrillte Verkettunger, Abh. Math. Sem. Hanischen Univ. 11 (1936), 171-178.
- J. H. Conway, An enumeration of knots and links, and some of their algebraic properties, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 329–358. MR 0258014
- H. S. M. Coxeter, Regular complex polytopes, Cambridge University Press, London-New York, 1974. MR 0370328
- F. A. Garside, The braid group and other groups, Quart. J. Math. Oxford Ser. (2) 20 (1969), 235–254. MR 248801, DOI 10.1093/qmath/20.1.235
- V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127 10. V. F. R. Jones, Braid groups, Hecke algebras and type II1 factors, Japan-U.S. Conf. Proc. 1983.
- Louis H. Kauffman, Formal knot theory, Mathematical Notes, vol. 30, Princeton University Press, Princeton, NJ, 1983. MR 712133
- Shin’ichi Kinoshita and Hidetaka Terasaka, On unions of knots, Osaka Math. J. 9 (1957), 131–153. MR 98386 13. J. Lannes, Sur l’invariant de Kervaire pour les noeuds classiques, École Polytechnique, Palaiseau, 1984 (preprint).
- J. Levine, Polynomial invariants of knots of codimension two, Ann. of Math. (2) 84 (1966), 537–554. MR 200922, DOI 10.2307/1970459 15. A. A. Markov, Uber die freie Aquivalenz geschlossener Zopfe, Mat. Sb. 1 (1935), 73-78.
- Kunio Murasugi, On closed $3$-braids, Memoirs of the American Mathematical Society, No. 151, American Mathematical Society, Providence, R.I., 1974. MR 0356023
- Kenneth A. Perko Jr., On the classification of knots, Proc. Amer. Math. Soc. 45 (1974), 262–266. MR 353294, DOI 10.1090/S0002-9939-1974-0353294-X
- Mihai Pimsner and Sorin Popa, Entropy and index for subfactors, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 1, 57–106. MR 860811, DOI 10.24033/asens.1504
- Robert T. Powers, Representations of uniformly hyperfinite algebras and their associated von Neumann rings, Ann. of Math. (2) 86 (1967), 138–171. MR 218905, DOI 10.2307/1970364
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
- Lee Rudolph, Nontrivial positive braids have positive signature, Topology 21 (1982), no. 3, 325–327. MR 649763, DOI 10.1016/0040-9383(82)90014-3 22. S. Svensson, Handbook of Seaman’s ropework, Dodd, Mead, New York, 1971.
- H. N. V. Temperley and E. H. Lieb, Relations between the “percolation” and “colouring” problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the “percolation” problem, Proc. Roy. Soc. London Ser. A 322 (1971), no. 1549, 251–280. MR 498284, DOI 10.1098/rspa.1971.0067
- Hans Wenzl, On sequences of projections, C. R. Math. Rep. Acad. Sci. Canada 9 (1987), no. 1, 5–9. MR 873400
Additional Information
- Journal: Bull. Amer. Math. Soc. 12 (1985), 103-111
- MSC (1980): Primary 57M25; Secondary 46L10
- DOI: https://doi.org/10.1090/S0273-0979-1985-15304-2
- MathSciNet review: 766964