no. 3
Combinatorics and topology - François Jaeger's work in knot theory
Annales de l'Institut Fourier, Tome 49 (1999) no. 3, pp. 927-953

François Jaeger found a number of beautiful connections between combinatorics and the topology of knots and links, culminating in an intricate relationship between link invariants and the Bose-Mesner algebra of an association scheme. This paper gives an introduction to this connection.

François Jaeger a découvert de très belles relations entre la combinatoire et la topologie des nœuds et entrelacs, la plus remarquable étant celle entre les invariants d’entrelacs et l’algèbre de Bose-Mesner d’un schéma d’association. Cet article introduit cette relation.

@article{AIF_1999__49_3_927_0,
     author = {Kauffman, Louis H.},
     title = {Combinatorics and topology - {Fran\c{c}ois} {Jaeger's} work in knot theory},
     journal = {Annales de l'Institut Fourier},
     pages = {927--953},
     year = {1999},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {49},
     number = {3},
     doi = {10.5802/aif.1700},
     zbl = {0922.57004},
     mrnumber = {2000g:57022},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1700/}
}
TY  - JOUR
AU  - Kauffman, Louis H.
TI  - Combinatorics and topology - François Jaeger's work in knot theory
JO  - Annales de l'Institut Fourier
PY  - 1999
SP  - 927
EP  - 953
VL  - 49
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1700/
DO  - 10.5802/aif.1700
LA  - en
ID  - AIF_1999__49_3_927_0
ER  - 
%0 Journal Article
%A Kauffman, Louis H.
%T Combinatorics and topology - François Jaeger's work in knot theory
%J Annales de l'Institut Fourier
%D 1999
%P 927-953
%V 49
%N 3
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1700/
%R 10.5802/aif.1700
%G en
%F AIF_1999__49_3_927_0
Kauffman, Louis H. Combinatorics and topology - François Jaeger's work in knot theory. Annales de l'Institut Fourier, Tome 49 (1999) no. 3, pp. 927-953. doi: 10.5802/aif.1700

[1] K. Reidemeister, Julius Springer, Berlin, 1932 ; Chelsea Pub. Co., New York, 1948.

[2] F. Jaeger, On Tutte polynomials and link polynomials, Proceedings AMS, 103, n° 2 (1988), 647-654. | Zbl | MR

[3] F. Jaeger, Graph colourings and link invariants, in Graph Colourings, R. Nelson and R.J. Wilson ed., Pitman Research Notes in Mathematics, Series 218, Longman Scientific and Technical, 1990, 97-114. | Zbl | MR

[4] F. Jaeger, Composition products and models for the Homfly polymomial, L'Enseignement Math., 35 (1989), 323-361. | Zbl | MR

[5] F. Jaeger, A combinatorial model for the Homfly polynomial, Europ. J. Combinatorics, 11 (1990), 549-558. | Zbl | MR

[6] F. Jaeger, D. Welsh, D. Vertigan, On the Computational Complexity of the Jones and Tutte polynomials, Proc. Cambridge Phil. Soc., 108 (1990), 5-53. | Zbl | MR

[7] F. Jaeger, Invariants de graphes matroïdes, nœuds: modèles et complexité, Actes des Journées du PRC Mathématiques et Informatique, Paris, 6-7 mars 1989, M. Las Vergnas éd., 86-105.

[8] F. Jaeger, Théorie des Nœuds et Combinatoire, Actes de la Deuxième Rencontre Franco-Algérienne de Recherche Opérationnelle, USTHB, mai 1992.

[9] F. Jaeger, Circuit partitions and the Homfly polynomial of closed braids, Trans. Am. Math. Soc., 323, n° 1 (1991), 449-463. | Zbl | MR

[10] F. Jaeger, Strongly regular graphs and spin models for the Kauffman polynomial, Geom. Dedicata, 44 (1992), 23-52. | Zbl | MR

[11] F. Jaeger, On the Kauffman polynomial of planar matroids, Proceedings of the Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity, Elsevier, 1992, 117-127. | Zbl | MR

[12] F. Jaeger, Plane graphs and link invariants, Discrete Math., 114 (1993), 253-264. | Zbl | MR

[13] F. Jaeger, Modèles à spins, invariants d'entrelacs et schémas d'association, Actes du Séminaire Lotharingien de Combinatoire, 30e session, R. Konig et V. Strehl éd., IRMA, Strasbourg (1993), 43-60.

[14] F. Jaeger, E. Bannai, A. Sali, Classification of small spin models, Kyushu J. Math., 48 (1994), 185-200. | Zbl | MR

[15] F. Jaeger, L. H. Kauffman, H. Saleur, The Conway polynomial in ℝ3 and in thickened surfaces: a new determinant formulation, J. Comb. Theory (B), 61, n° 2 (1994), 237-259. | Zbl | MR

[16] F. Jaeger, On spin models, triply regular association schemes, and duality, J. Algebraic Comb., 4, n° 2 (1995), 103-144. | Zbl | MR

[17] F. Jaeger, Spin models for link invariants, in Surveys in Combinatorics 1995, Peter Rowlinson ed., London Mathematical Society Lecture Notes Series 218, Cambridge University Press, 1995, 71-101. | Zbl | MR

[18] F. Jaeger, Towards a classification of spin models in terms of association schemes, in Progress in Algebraic Combinatorics, Advanced Studies in Pure Mathematics 24, Mathematical Society of Japan, 1996, 197-225. | Zbl | MR

[19] F. Jaeger, New constructions of models for link invariants, Pacific J. Math., 176, n° 1 (1996). | Zbl | MR

[20] W.B.R. Lickorish, K.C. Millett, A polynomial invariant for oriented links, Topology, 26 (1987), 107-141. | Zbl | MR

[21] V.F.R. Jones, On knot invariants related to some statistical mechanics models, Pacific J. Math., 137, n° 2 (1989), 311-334. | Zbl | MR

[22] L.H. Kauffman, State Models and the Jones Polynomial, Topology, 26 (1987), 395-407. | Zbl | MR

[23] L.H. Kauffman, Statistical Mechanics and the Jones Polynomial, Contemp. Math. Pub., Am. Math. Soc., 78 (1988), 263-297. | Zbl | MR

[24] L.H. Kauffman, An invariant of regular isotopy, Trans. Am. Math. Soc., 318, n° 2 (1990), 417-471. | Zbl | MR

[25] L.H. Kauffman, State models for link polynomials, Enseignement Math., 36 (1990), 1-37. | Zbl | MR

[26] L.H. Kauffman, A Tutte polynomial for signed graphs, Discrete Appl. Math., 25 (1989), 105-127. | Zbl | MR

[27] L.H. Kauffman, Knots and Physics, World Scientific Publishers, 1991 ; second ed., 1993 (723 pages). | Zbl

[28] J. Goldman, L.H. Kauffman, Knots tangles and electrical networks, Advances Applied Math., 14 (1993), 267-306. | Zbl | MR

[29] P. De La Harpe, Spin models for link polynomials, strongly regular graphs and Jaeger's Higman-Sims model, Pacific J. Math., 162, n° 1 (1994), 57-96. | Zbl | MR

[30] Eiichi Bannai, Etsuko Bannai, Association schemes and spin models (a survey), Lecture Notes — Pure Math. Symposium, Postech, Pohang, Korea, 1993, 16 pages.

[31] Eiichi Bannai, Etsuko Bannai, Generalized spin models (four weight spin models), Pacific J. Math., 170, n° 1 (1995), 1-16. | Zbl | MR

[32] K. Nomura, An algebra associated with a spin model, J. Algebraic Combinatorics, 6 (1997), 53-58. | Zbl | MR

[33] M. Aigner, J.J. Seidel, Knoten, spin modelle und graphen, Jber. d. Dr. Math.-Verein., 97 (1995), 75-96. | Zbl | MR

Cité par Sources :