Bulletin of the American Mathematical Society

Full text of review: PDF   This review is available free of charge.
Book Information:

Author: V. G. Turaev
Title: Quantum invariants of knots and 3-manifolds
Additional book information: de Gruyter Studies in Mathematics, vol. 18, Walter de Gruyter, Berlin, 1994, x + 588 pp., ISBN 3-11-013704-6, $118.95 (DM 288)$

Henning Haahr Andersen, Tensor products of quantized tilting modules, Comm. Math. Phys. 149 (1992), no. 1, 149–159. MR 1182414

V. G. Drinfel′d, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 798–820. MR 934283

V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127

Louis H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), no. 3, 395–407. MR 899057, DOI 10.1016/0040-9383(87)90009-7

George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 1227098

N. Yu. Reshetikhin and V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990), no. 1, 1–26. MR 1036112

N. Reshetikhin and V. G. Turaev, Invariants of $3$-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547–597. MR 1091619, DOI 10.1007/BF01239527

V. G. Turaev and O. Ya. Viro, State sum invariants of $3$-manifolds and quantum $6j$-symbols, Topology 31 (1992), no. 4, 865–902. MR 1191386, DOI 10.1016/0040-9383(92)90015-A

V. Turaev and H. Wenzl, Quantum invariants of $3$-manifolds associated with classical simple Lie algebras, Internat. J. Math. 4 (1993), no. 2, 323–358. MR 1217386, DOI 10.1142/S0129167X93000170

Edward Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399. MR 990772

1

H. H. Andersen. Tensor products of quantized tilting modules. Comm. Math. Phys. 149:149--159, 1992. MR 94b:17015

2

V. Drinfel'd. Quantum groups. In Proceedings of the International Congress of Mathematicians, volume 1, pages 798--820, Berkeley, California, 1986. MR 89f:17017

3

V. F. R. Jones. Index of subfactors. Invent. Math. 72:1--25, 1983. MR 84d:46097

4

L. H. Kauffman. State models and the Jones polynomial. Topology 26:395--407, 1987. MR 88f:57006

5

G. Lusztig. Introduction to quantum groups. Progress in Math., vol. 110, Birkhäuser, Boston-Basel-Stuttgart, 1993. MR 94m:17016

6

N. Yu. Reshetikhin and V. G. Turaev. Ribbon graphs and their invariants derived from quantum groups. Comm. Math. Phys. 127:1--26, 1990. MR 91c:57016

7

N. Yu. Reshetikhin and V. G. Turaev. Invariants of -manifolds via link polynomials and quantum groups. Invent. Math. 103:547--597, 1991. MR 92b:57024

8

V. G. Turaev and O. Y. Viro. State sum invariants of -manifolds and quantum -symbols. Topology 31:865--902, 1992. MR 94d:57044

9

V. G. Turaev and H. Wenzl. Quantum invariants of -manifolds associated with classical simple Lie algebras. Internat. J. Math. 4:323--358, 1993. MR 94i:57019

10

E. Witten. Quantum field theory and the Jones polynomial. Comm. Math. Phys. 121:351--399, 1989. MR 90h:57009