New invariants in the theory of knots

Kauffman, Louis H.

On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986, Astérisque, no. 163-164 (1988), pp. 137-219.

Zbl: 0673.57007

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     author = {Kauffman, Louis H.},
     title = {New invariants in the theory of knots},
     booktitle = {On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {163-164},
     year = {1988},
     zbl = {0673.57007},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1988__163-164__137_0/}
}

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Kauffman, Louis H. New invariants in the theory of knots, in On the Geometry of Differentiable Manifolds Rome, 23-27 juin 1986, Astérisque, no. 163-164 (1988), pp. 137-219. http://archive.numdam.org/item/AST_1988__163-164__137_0/

References
Cited by

[A] J. W. Alexander. Topological invariants of knots and links. Trans. Amer. Math. Soc., 30 (1923), 275-306. | DOI | JFM

[B] R. J. Baxter. Exactly Solved Models in Statistical Mechanics. Academic Press (1982). | Zbl

[Bir] Joan S. Birman. Braids, links and mapping class groups. Ann. of Math. Studies, No. 82. Princeton University Press, Princeton, New Jersey (1976). | Zbl

[BW] Joan S. Birman and Hans Wenzel. Link polynomials and a new algebra. (preprint).

[BLM] R. Brandt, W.B.R. Lickorish and K.C. Millett. A polynomial invariant for unoriented knots and links. Invent. Math., 84, 563-573 (1986). | DOI | EuDML | Zbl

[Con] J. H. Conway. An enumeration of knots and links and some of their algebraic properties. Computational Problems in Abstract Algebra. Pergamon Press, New York (1970), 329-358. | Zbl

[Co] Daryl Cooper. Thesis. Warwick (1981).

[Cr] R. H. Crowell. Genus of alternating link types. Ann. of Math., 69 (1959), 258-275. | DOI | Zbl

[CF] R. H. Crowell and R. H. Fox. Introduction to Knot Theory. Blaisdell Publishing Company (1963). | Zbl

[G] C. Giller. A family of links and the Conway calculus. Trans. Amer. Math. Soc., 270 (1982), 75-109. | DOI | Zbl

[Gr] W. Graeub. Die semilinearen abbildungen. S.B. Heidelberger Akad. Wiss. Math. - Nat. K1. (1950). 205-272. | Zbl

[H] C. H. Ho. A new polynomial invariant for knots and links - preliminary report. AMS Abstracts, Vol. 6, #4, Issue 39(1985), 300.

[Homfly] P. Freyd, D. Yetter, J. Hoste, W. Lickorish, K. Millett, and A. Ocneanu. A new polynomial invariant of knots and links. Bull. Amer. Math. Soc., 12 (1985), 239-246. | DOI | Zbl

[J1] V. F. R. Jones. A new knot polynomial and von Neumann algebras. Notices of AMS (1985).

[J2] V. F. R. Jones. A polynomial invariant for links via von Neumann algebras. Bull. Amer. Math. Soc, 12 (1985), 103-112. | DOI | Zbl

[J3] V. F. R. Jones. Hecke algebra representations of braid groups and links polynomials, (to appear). | Zbl

[K1] L. H. Kauffman. The Conway polynomial. Topology, 20(1980), 101-108. | DOI | Zbl

[K2] L. H. Kauffman. Formal Knot Theory. Princeton University Press. | Zbl

[K3] L. H. Kauffman. On Knots. Princeton University Press. Annals Study 115 (1987). | Zbl

[K4] L. H. Kauffman. An Invariant of Regular Isotopy. (Announcement - 1985) . | Zbl

[K5] L. H. Kauffman. State models and the Jones polynomial. Topology 26 No. 3 (1987). 395-407. | DOI | Zbl

[K6] L. H. Kauffman. An invariant of regular isotopy. (to appear). | DOI | Zbl

[K7] L. H. Kauffman. Knots and Physics. (in preparation).

[K8] L. H. Kauffman. Invariants of graphs in three space. (to appear). | DOI | Zbl

[K9] L. H. Kauffman. A Tutte polynomial for signed graphs. (to appear). | DOI | Zbl

[K10] L. H. Kauffman and I. Handler. State expansions and generalized Tutte polynomials. (in preparation).

[K11] L. H. Kauffman. Statistical mechanics and the Jones polynomial. (To appear in the Proceedings of the 1986 Summer Conference on the Artin Braid Group, Santa Cruz, California.) | Zbl

[K12] L. H. Kauffman. State models and knot polynomials - an introduction. (To appear in the Proceedings of the 1987 Summer meeting of the Brasilian Mathematical Society - IMPA - Rio de Janeiro, Brazil.) | Zbl

[Ki] M. Kidwell. On the degree of the Brandt-Lickorish-Millett polynomial of a Link. (preprint). | Zbl

[LM] W. B. R. Lickorish and K. C. Millett. A polynomial invariant of oriented links. Topology vol. 26, No. ]. 107-141. | DOI | Zbl

[L] W. B. R. Lickorish. A relationship between link polynomials. Math. Proc. Cambridge Philos. Soc., (to appear). | Zbl

[M1] K. Murasugi. Jones polynomials and classical conjectures in knot theory I. (to appear). | Zbl

K. Murasugi. Jones polynomials and classical conjectures in knot theory II. (to appear). | DOI | Zbl

[M2] K. Murasugi. Jones polynomials and class conjectures in knot theory. Topology, vol. 26, No. 2 (1987), 187-194. | DOI | Zbl

[P] R. Penrose. Applications of negative dimensional tensors. Combinatorial Mathematics and its Applications. Edited by D.J.A. Welsh. Academic Press (1971). | Zbl

[Ro] D. Rolfsen. Knots and Links. Publish or Perish Press (1976). | Zbl

[S] J. Simon. Topological chirality of certain molecules. Topology vol. 25, No. 2, pp. 229-235 (1986). | DOI | Zbl

[M] H. Morton. Seifert Circles and Knot Polynomials. Math. Proc. Comb. Phil. Soc., 99 (1986), pp. 107-109. | DOI | Zbl

[T1] M. Thistlethwaite. A spanning tree expansion of the Jones polynomial. Topology, vol. 26, No. 3 (1987), 297-310. | DOI | Zbl

[T2] M. Thistlethwaite. Kauffman's polynomial and alternating links. (to appear). | DOI | Zbl

[Tu] W. T. Tutte, A contribution to the theory of chromatic polynomials. Canad. J. Math., 6 (1953), 80-91. | DOI | Zbl

[W] K. Wolcott. The knotting of theta curves and other graphs in $S^{3}$ . (to appear in Proceedings of 1985 Georgia Topology Conference). | Zbl

[Wu] Y. Q. Wu. Jones polynomial and the crossing number of links. (preprint). | Zbl

[Wh] J. White. Self-linking and the Gauss integral in higher dimensions. Amer. J. Math. XCI (1969), 693-728. | DOI | Zbl

[BCW] William R. Bauer, F. H. C. Crick and James H. White. Supercoiled DNA. Sci. Am., 243 (1980), pp. 118-133.

[F] F. B. Fuller. Decomposition of the linking number of a closed ribbon: A problem from molecular biology. Proc. Natl. Acad. Sci., USA, 75 (1978), 3557. | DOI | Zbl