Abstract

In this article we shall give an account of certain developments in knot theory which followed upon the discovery of the Jones polynomial [Jo3] in 1984. The focus of our account will be recent glimmerings of understanding of the topological meaning of the new invariants. A second theme will be the central role that braid

Citations

504	Quantum field theory and the Jones polynomial - Witten - 1989
235	Invariants of 3-manifolds via link polynomials and quantum groups - Reshetikhin, Turaev - 1991
219	A q-difference analogue of U(G) and the Yang-Baxter equation - Jimbo - 1985
214	Index for subfactors - Jones - 1983
197	Dehn surgery on knots - Gordon - 1990
182	links and mapping class groups - Birman, Braids - 1974
128	Cohomology of knot spaces, Theory of Singularities and its Applications - Vassiliev - 1990
122	An enumeration of knots and links, and some of their algebraic properties, Computation problems in abstract algebra - Conway - 1969
104	The 3–manifold invariants of Witten and Reshetikhin– Turaev for sl(2 - Kirby, Melvin - 1991
98	An invariant of regular isotopy - Kauffman - 1990
95	Ocneanu, A new polynomial invariant of knots and - Freyd, Yetter, et al. - 1992
91	Knots are determined by their complements - Gordon, Luecke - 1989
89	G.: Solutions of the classical Yang-Baxter equations for simple Lie algebras. Funkts. Anal. i ego Prilozh - Belavin, Drinfeld - 1982
84	Vassiliev’s knot invariants, Adv - Kontsevich - 1993
79	curves associated to character varieties of 3–manifolds, Invent - Cooper, Culler, et al. - 1994
79	The Yang–Baxter equation and invariants of links - Turaev - 1988
76	Polynomials and a New Algebra - Birman, Wenzl, et al.
72	polynomial and classical conjectures in knot theory, preprint 1985 - Murasugi, Jones
70	Knots and links. Publish or - Rolfsen - 1976
64	Topological invariants of knots and links - Alexander - 1928
61	Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation - Jeffrey - 1992
57	The invariant theory of n × n matrices - Procesi - 1976
55	A lemma on systems of knotted curves - Alexander - 1963
47	Monodromy representations of braid groups and Yang-Baxter equations, Ann. Inst. Fourier 37 - Kohno - 1987
46	Exactly solvable models in statistical mechanics - Baxter
45	Quantum groups and subfactors of type - Wenzl - 1990
43	Möbius energy of knots and unknots - Freedman, He, et al. - 1994
43	Algorithms for the complete decomposition of a closed 3-manifold - Jaco, Tollefson - 1995
35	Studying links via closed braids III: Classifying links which are closed 3-braids - Birman, Menasco - 1993
32	Homological representations of the Hecke algebra - Lawrence - 1990
31	Linear representations of braid groups and classical Yang-Baxter equations - Kohno - 1986
31	Quasitriangular Hopf algebras and invariants of tangles - Reshetikhin
28	and Ping Xu Classical Solution of the Quantum Yang-Baxter Equation - Weinstein - 1992
25	On the classification of homeomorphisms of 2-manifolds and the classification of 3-manifolds - Hemion - 1979
25	polynomials and a graphical calculus - Kauffman, Vogel, et al. - 1992
21	invariants of finite type and perturbation - Baez, Link - 1992
21	Braids and the Jones polynomial - Franks, Williams - 1987
20	Non-invertible knots exist, Topology 2 - Trotter - 1963
19	Vertex models, quantum groups and Vassiliev knot invariants - Lin - 1991
18	Theorie der Zöpfe, Hamburg Abh - Artin - 1925
16	Knot polynomials and Vassiliev’s invariants, Invent - Birman, Lin - 1993
15	Threading knot diagrams - Morton - 1986
14	On invariants of torus knots derived from quantum groups - Jones, Rosso - 1993
13	algebra representations of braid groups and link polynomials - Hecke
11	Constant quasiclassical solutions of the quantum Yang-Baxter equation - Drinfeld - 1983
10	Über die freie Äquivalenz geschlossener Zöpfe - Markov - 1935
9	knot invariants related to some statistical mechanical models - On
9	Infinitely many knots with the same polynomial invariant - Kanenobu
7	Groupes quantiques et modèles à vertex de V. Jones en théorie des noeuds - Rosso - 1988
6	Group invariants of links. Topology 31 - Wada - 1992