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Book Review

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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)

References [Enhancements On Off] (What's this?)

  • 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

Review Information:

Reviewer: Greg Kuperberg
Affiliation: Yale University
Email: greg@math.yale.edu
Journal: Bull. Amer. Math. Soc. 33 (1996), 107-110
DOI: https://doi.org/10.1090/S0273-0979-96-00621-0
Review copyright: © Copyright 1996 American Mathematical Society
American Mathematical Society