A categorification of the Jones polynomial

S. Akbulut and J. McCarthy, <i>Casson's Invariant for Oriented Homology $3$-spheres---An Exposition</i>, Math. Notes <b>36</b>, Princeton Univ. Press, Princeton, 1990.

A. A. Beilinson, G. Lusztig, and R. MacPherson, <i>A geometric setting for the quantum deformation of $\mathrm{GL}_n$</i>, Duke Math. J. <b>61</b> (1990), 655--677.

J. Bernstein, I. Frenkel, and M. Khovanov, <i>A categorification of the Temperley-Lieb algebra and Schur quotients of $U(\mf{sl}_2)$ by projective and Zuckerman functors</i>, to appear in Selecta Math. (N.S.).

J. S. Carter and M. Saito, <i>Reidemeister moves for surface isotopies and their interpretation as moves to movies</i>, J. Knot Theory Ramifications <b>2</b> (1993), 251--284.

L. Crane and I. B. Frenkel, <i>Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases</i>, J. Math. Phys. <b>35</b> (1994), 5136--5154.

J. Fischer, <i>2-categories and 2-knots</i>, Duke Math. J. <b>75</b> (1994), 493--526.

A. Floer, <i>An instanton-invariant for 3-manifolds</i>, Comm. Math. Phys. <b>118</b> (1988), 215--240.

I. B. Frenkel and M. Khovanov, <i>Canonical bases in tensor products and graphical calculus for $U_q(\mathfrak{sl}_2)$</i>, Duke Math. J. <b>87</b> (1997), 409--480.

I. Grojnowski and G. Lusztig, ``On bases of irreducible representations of quantum $\mathrm{GL}_n$'' in <i>Kazhdan-Lusztig Theory and Related Topics (Chicago, Ill., 1989)</i>, Contemp. Math. <b>139</b>, Amer. Math. Soc., Providence, 1992, 167--174.

F. Jaeger, D. L. Vertigan, and D. J. A. Welsh, <i>On the computational complexity of the Jones and Tutte polynomials</i>, Math. Proc. Cambridge. Philos. Soc. <b>108</b> (1990), 35--53.

V. F. R. Jones, <i>A polynomial invariant for knots via von Neumann algebras</i>, Bull. Amer. Math. Soc. (N.S.) <b>12</b> (1985), 103--111.

L. H. Kauffman, <i>State models and the Jones polynomial</i>, Topology <b>26</b> (1987), 395--407.

M. Khovanov, <i>Graphical calculus, canonical bases and Kazhdan-Lusztig theory</i>, Ph.D. thesis, Yale University, 1997.

W. B. R. Lickorish and M. B. Thistlethwaite, <i>Some links with nontrivial polynomials and their crossing-numbers</i>, Comment. Math. Helv. <b>63</b> (1988), 527--539.

G. Lusztig, <i>Introduction to Quantum Groups</i>, Progr. Math. <b>110</b>, Birkhäuser, Boston, 1993.

H. Murakami, <i>Quantum $\mathrm{SU}(2)$-invariants dominate Casson's $\mathrm{SU}(2)$-invariant</i>, Math. Proc. Cambridge Philos. Soc. <b>115</b> (1994), 253--281.

G. Meng and C. H. Taubes, <i>${\underline{SW}}=$ Milnor torsion</i>, Math. Res. Lett. <b>3</b> (1996), 661--674.

M. B. Thistlethwaite, <i>On the Kauffman polynomial of an adequate link</i>, Invent. Math. <b>93</b> (1988), 285--296.