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Book Review

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Book Information

Author(s): 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, $118.95 (DM 288), ISBN 3-11-013704-6

References:

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 $3$-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 $3$-manifolds and quantum $6j$-symbols. Topology 31:865--902, 1992. MR 94d:57044

9
V. G. Turaev and H. Wenzl. Quantum invariants of $3$-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

Additional Information:

Reviewer(s):
Greg Kuperberg
Affiliation: Yale University
Email: greg@math.yale.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 33 (1996), 107-110.
DOI: 10.1090/S0273-0979-96-00621-0
PII: S 0273-0979(96)00621-0
Copyright of article: Copyright 1996, American Mathematical Society

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