Skein quantization of Poisson algebras of loops on surfaces
Annales scientifiques de l'École Normale Supérieure (1991)
- Volume: 24, Issue: 6, page 635-704
- ISSN: 0012-9593
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topTuraev, Vladimir G.. "Skein quantization of Poisson algebras of loops on surfaces." Annales scientifiques de l'École Normale Supérieure 24.6 (1991): 635-704. <http://eudml.org/doc/82308>.
@article{Turaev1991,
author = {Turaev, Vladimir G.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {skein invariants of 3-manifolds; Jones polynomial; Poisson algebras of loops on surfaces; quantization; Lie bialgebras; Poisson Lie groups; set of free homotopy classes of loops; skein module; Wilson loop observables; infinitesimal Poisson Lie group; bi-Poisson bialgebras; biquantization},
language = {eng},
number = {6},
pages = {635-704},
publisher = {Elsevier},
title = {Skein quantization of Poisson algebras of loops on surfaces},
url = {http://eudml.org/doc/82308},
volume = {24},
year = {1991},
}
TY - JOUR
AU - Turaev, Vladimir G.
TI - Skein quantization of Poisson algebras of loops on surfaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1991
PB - Elsevier
VL - 24
IS - 6
SP - 635
EP - 704
LA - eng
KW - skein invariants of 3-manifolds; Jones polynomial; Poisson algebras of loops on surfaces; quantization; Lie bialgebras; Poisson Lie groups; set of free homotopy classes of loops; skein module; Wilson loop observables; infinitesimal Poisson Lie group; bi-Poisson bialgebras; biquantization
UR - http://eudml.org/doc/82308
ER -
References
top- [1] V. G. DRINFELD, Hamiltonian Structures on Lie Groups, Lie Bialgebras and the Meaning of the classical Yang-Baxter Equation (Doklady A.N. S.S.S.R., Vol. 268, 1982, pp. 285-287 ; English translation : Soviet Math. Dokl., Vol. 27, No. 1, 1983). Zbl0526.58017MR84i:58044
- [2] V. G. DRINFELD, Quantum Groups (Proc. Internat. Congress Math., Berkeley, 1986, Amer. Math. Soc., Providence, R.I., 1987, pp. 798-820). Zbl0667.16003MR89f:17017
- [3] W. M. GOLDMAN, The Symplectic Nature of Fundamental Groups of Surfaces (Adv. Math., Vol. 54, 1984, pp. 200-225). Zbl0574.32032MR86i:32042
- [4] W. M. GOLDMAN, Invariant Functions on Lie Groups and Hamiltonian Flows of Surface Group Representations (Invent. Math., Vol. 85, 1986, pp. 263-302). Zbl0619.58021MR87j:32069
- [5] J. HOSTE and M. K. KIDWELL, Dichromatic Link Invariants, (Trans. Amer. Math. Soc., Vol. 321, 1990, pp. 197-229). Zbl0702.57002MR90m:57007
- [6] F. JAEGER, Composition Products and Models for the Homfly Polynomial, preprint, Grenoble, 1988. Zbl0705.57004
- [7] L. H. KAUFFMAN, New Invariants in the Theory of Knots (Am. Math. Mon., Vol. 95, 1988, pp. 195-242). Zbl0657.57001MR89d:57005
- [8] M. KONTSEVICH, Rational Conformal Field Theory and Invariants of 3-Manifolds, preprint, 1989.
- [9] W. B. R. LICKORISH, Polynomials for Links (Bull. London Math. Soc., Vol. 20, 1988, pp. 558-588). Zbl0685.57001MR90d:57004
- [10] W. B. R. LICKORISH and K. C. MILLETT, A Polynomial Invariant of Oriented Links (Topology, Vol. 26, 1987, pp. 107-141). Zbl0608.57009MR88b:57012
- [11] J. H. PRZYTYCKI, Skein Modules of 3-manifolds, preprint, 1987.
- [12] N. Y. RESHETIKHIN, Quantized Universal Enveloping Algebras, the Yang-Baxter Equation and Invariants of Links, I and II, L.O.M.I. preprints E-4-87 and E-17-87, Leningrad, 1988.
- [13] N. Y. RESHETIKHIN and V. G. TURAEV, Invariants of 3-manifolds via Link Polynomials and Quantum Groups, (Invent. Math., Vol. 103, 1991, pp. 547-597). Zbl0725.57007MR92b:57024
- [14] M. A. SEMENOV-TIAN-SHANSKY, Dressing Transformations and Poisson Group Actions (Publ. Res. Inst. Math. Sci. Kyoto Univ., Vol. 21, 1985, pp. 1237-1260). Zbl0674.58038MR88b:58057
- [15] J.-P. SERRE, Lie Algebras and Lie Groups, Benjamin, New York-Amsterdam, 1965. Zbl0132.27803MR36 #1582
- [16] V. G. TURAEV, Intersections of Loops in Two-Dimensional Manifolds (Matem. Sbornik, Vol. 106, 1978, pp. 566-588 ; English translation : Math. U.S.S.R. Sbornik, Vol. 35, 1979, pp. 229-250). Zbl0422.57005MR80d:57019
- [17] V. G. TURAEV, Multivariable Generalizations of the Seifert form of Classical Knot (Matem. Sbornik, Vol. 116, 1981, pp. 370-397 ; English translation : Math. U.S.S.R. Sbornik, (Vol. 44, 1983, pp. 335-361). Zbl0508.57005
- [18] V. G. TURAEV, The Yang-Baxter Equation and Invariants of Links (Invent. Math., Vol. 92, 1988, pp. 527-553). Zbl0648.57003MR89e:57003
- [19] V. G. TURAEV, The Conway and Kauffman Modules of the Solid Torus (Zap. nauchn. sem. L.O.M.I., Vol. 167, 1988, pp. 79-89 ; English translation : J. Soviet. Math.). Zbl0673.57004MR90f:57012
- [20] V. G. TURAEV, Algebras of Loops on Surfaces, Algebras of Knots and Quantization, preprint L.O.M.I., Leningrad, 1988.
- [21] J.-L. VERDIER, Groupes quantiques (d'après V. G. Drinfel'd) (Astérisque, Vol. 152-153, 1987, pp. 305-319). Zbl0645.16006MR89f:17021
- [22] E. WITTEN, Quantum Field Theory and the Jones Polynomial, (Comm. Math. Phys., Vol. 121, 1989, pp. 351-399). Zbl0667.57005MR90h:57009
- [23] S. WOLPERT, On the Symplectic Geometry of Deformations of Hyperbolic Surface (Ann. Math., Vol. 117, 1983, pp. 207-234). Zbl0518.30040MR85e:32028
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