Quantum invariants of links and 3-valent graphs in 3-manifolds
Publications Mathématiques de l'IHÉS, Tome 77 (1993), pp. 121-171 
@article{PMIHES_1993__77__121_0,
     author = {Turaev, Vladimir},
     title = {Quantum invariants of links and 3-valent graphs in 3-manifolds},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {121--171},
     year = {1993},
     publisher = {Institut des Hautes Etudes Scientifiques},
     volume = {77},
     mrnumber = {1249172},
     zbl = {0822.57012},
     language = {en},
     url = {https://www.numdam.org/item/PMIHES_1993__77__121_0/}
}
TY  - JOUR
AU  - Turaev, Vladimir
TI  - Quantum invariants of links and 3-valent graphs in 3-manifolds
JO  - Publications Mathématiques de l'IHÉS
PY  - 1993
SP  - 121
EP  - 171
VL  - 77
PB  - Institut des Hautes Etudes Scientifiques
UR  - https://www.numdam.org/item/PMIHES_1993__77__121_0/
LA  - en
ID  - PMIHES_1993__77__121_0
ER  - 
%0 Journal Article
%A Turaev, Vladimir
%T Quantum invariants of links and 3-valent graphs in 3-manifolds
%J Publications Mathématiques de l'IHÉS
%D 1993
%P 121-171
%V 77
%I Institut des Hautes Etudes Scientifiques
%U https://www.numdam.org/item/PMIHES_1993__77__121_0/
%G en
%F PMIHES_1993__77__121_0
Turaev, Vladimir. Quantum invariants of links and 3-valent graphs in 3-manifolds. Publications Mathématiques de l'IHÉS, Tome 77 (1993), pp. 121-171. https://www.numdam.org/item/PMIHES_1993__77__121_0/

[A1] J. W. Alexander, The combinatorial theory of complexes, Ann. Math. (2), 31 (1930), 294-332. | JFM

[AW] R. Askey, J. Wilson, A set of orthogonal polynomials that generalize the Racah coefficients or 6 - j symbols, SIAM J. Math. Anal., 10, No. 5 (1979), 1008-1016. | Zbl | MR

[At] M. Atiyah, Topological quantum field theories, Publ. Math. IHES, 68 (1989), 175-186. | Zbl | MR | Numdam

[BL] L. C. Biedenharn, J. D. Louck, Angular momentum in quantum physics. Theory and application. Encyclopedia of Math. and its applications, v. 8, London, Reading, Amsterdam, Addison-Wesley Publ. Company (1981). | Zbl | MR

[J] V. F. R. Jones, Polynomial invariants of knots via von Neumann algebras, Bull. Amer. Math. Soc., 12 (1985), 103-111. | Zbl | MR

[K] L. M. Kauffman, State models and the Jones polynomial, Topology, 26 (1987), 395-407. | Zbl | MR

[KR1] A. N. Kirillov, N. Y. Reshetikhin, Representations of the algebra Uq(sl2), q-orthogonal polynomials and invariants of links, in V. G. KAC (ed.), Infinite dimensional Lie algebras and groups (Adv. Ser. In Math. Phys., vol. 7), World Scientific, Singapore (1988), 285-339. | Zbl | MR

[M] S. V. Matveev, Transformations of special spines and the Zeeman conjecture, Math. USSR Izvestia, 31 (1988), 423-434. | Zbl | MR

[P] R. Piergallini, Standard moves for standard polyhedra and spines, Rend. Circ. Mat. Palermo, 37, suppl. 18 (1988), 391-414. | Zbl | MR

[Re] K. Reidemeister, Knotentheorie, Ergebn. Math. Grenzgeb. 1 (1932), Berlin, Springer Verlag ; English translation : Knot theory, Moscow, Idaho, USA BSC Associates, (1983). | Zbl | JFM

[RT1] N. Y. Reshetikhin, V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Commun. Math. Phys., 127 (1990), 1-26. | Zbl | MR

[RT2] N. Y. Reshetikhin, V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math., 103 (1991), 547-598. | Zbl | MR

[RS] C. P. Rourke, B. J. Sanderson, Introduction to Piecewise-Linear Topology, Ergebn. Math. Grenzgeb., 69 (1972), Berlin, Heidelberg, New York, Springer-Verlag. | Zbl | MR

[T1] V. G. Turaev, The Yang-Baxter equations and invariants of links, Invent. Math., 92 (1988), 527-553. | Zbl | MR

[T2] V. G. Turaev, Shadow links and IRF-models of statistical mechanics, J. Diff. Geom., 36 (1992), 35-74. | Zbl | MR

[T3] V. G. Turaev, Quantum invariants of 3-manifolds and a glimpse of shadow topology, C. R. Acad. Sci. Paris, 313, serie I (1991), 395-398. | Zbl | MR

[T4] V. G. Turaev, Topology of shadows, preprint (1991).

[T5] V. G. Turaev, Introduction to modular categories and new invariants of 3-manifolds (in preparation).

[TV] V. G. Turaev and O. Y. Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology, 31 (1992), 865-902. | Zbl | MR

[Wa] K. Walker, On Witten's 3-manifolds invariant, preprint (1991).

[W1] E. Witten, Quantum field theory and Jones polynomial, Comm. Math. Phys., 121 (1989), 351-399. | Zbl | MR

[W2] E. Witten, Gauge theories, vertex models and quantum groups, Nuclear Physics B, 330 (1990), 285-346. | MR