Lie algebras and the Four Color Theorem

Abstract

We present a statement about Lie algebras that is equivalent to the Four Color Theorem.

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References

  1. [1]

    K. I. Appel, andW. Haken:Every planar map is four colorable, Contemp. Math.98, Amer. Math. Soc., Providence 1989.

    Google Scholar 

  2. [2]

    S. Axelrod, andI.M. Singer:Chern-Simons perturbation theory, Proc. XXth DGM Conference (New York, 1991) (S. Catto and A. Rocha, eds.), World Scientific, 1992, 3–45.

  3. [3]

    S. Axelrod, andI.M. Singer: Chern-Simons perturbation theory II,Jour. Diff. Geom.,39 (1994), 173–213.

    Google Scholar 

  4. [4]

    D. Bar-Natan:Perturbative aspects of the Chern-Simons topological quantum field theory, Ph.D. thesis, Princeton Univ., June 1991, Dep of Mathematics.

  5. [5]

    D. Bar-Natan:Weights of Feynman diagrams and the Vassiliev knot invariants, February 1991, preprint.

  6. [6]

    D. Bar-Natan: On the Vassiliev knot invariants,Topology,34 (1995), 423–472.

    Google Scholar 

  7. [7]

    D. Bar-Natan:Bibliography of Vassiliev Invariants, http://www.ma.huji.ac.il/≈drorbn.

  8. [8]

    D. Bar-Natan, andS. Garoufalidis: On the Melvin-Morton-Rozansky Conjecture,Invent. Math.,125 (1996), 103–133.

    Google Scholar 

  9. [9]

    J. A. Bondy, andU. S. R. Murty:Graph theory with applications, Elsevier, New York 1976.

    Google Scholar 

  10. [10]

    S. Garoufalidis, andT. Ohtsuki:On finite type 3-manifold invariants III: manifold weight systems, MIT and Tokyo Inst. of Tech. preprint, August 1995.

  11. [11]

    L. H. Kauffman: Map coloring and the vector cross-product,J. Comb. Theory, B 48 (1990), 145–154.

    Google Scholar 

  12. [12]

    L. H. Kauffman: Map coloring, q-deformed spin networks and Turaev-Viro invariants for 3-manifolds,Int. J. of Mod. Phys., B6 (1992), 1765–1794.

    Google Scholar 

  13. [13]

    L. H. Kauffman, andH. Saleur: An algebraic approach to the planar coloring problem,Commun. Math. Phys.,152 (1993), 565–590.

    Google Scholar 

  14. [14]

    A. S. Lipson: Link signature, Goeritz matrices, and polynomial invariants,L'Enseignement Math.,36 (1990), 93–114.

    Google Scholar 

  15. [15]

    T. Ohtsuki: Finite type invariants of integral homology 3-spheres,J. of Knot Theory and its Ramifications,5(1) (1996), 101–115.

    Google Scholar 

  16. [16]

    R. Penrose:Applications of negative dimensional tensors, Combinatorial mathematics and its applications (D. J. A. Welsh, ed), Academic Press, San-Diego 1971, 221–244.

    Google Scholar 

  17. [17]

    L. Rozansky:The trivial connection contribution to Witten's invariant and finite type invariants of rational homology spheres, q-alg/9503011 preprint, March 1995.

  18. [18]

    T. L. Saaty, andP. C. Kainen:The four color problem, assaults and conquest, McGraw-Hill, New-York 1977.

    Google Scholar 

  19. [19]

    P. G. Tait: Remarks on colourings of maps,Proc Royal Soc. Edinburgh Ser. A.,10 (1880), 729.

    Google Scholar 

  20. [20]

    H. Whitney: A set of topological invariants for graphsAmer. J. Math.,55 (1933), 231–235.

    Google Scholar 

  21. [21]

    H. Whitney: On the classification of graphs,Amer. J. Math.,55 (1933), 236–244.

    Google Scholar 

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Bar-Natan, D. Lie algebras and the Four Color Theorem. Combinatorica 17, 43–52 (1997). https://doi.org/10.1007/BF01196130

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Mathematics Subject Classification (1991)

  • 05 C 05
  • 17 B 20
  • 57 M 15