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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 3090428
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: S. Chmutov, S. Duzhin and J. Mostovoy
Title: Introduction to Vassiliev knot invariants
Additional book information: Cambridge University Press, Cambridge, 2012, xvi+504 pp., ISBN 978-1-107-02083-2, US $70.00., hardcover

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

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  • D. Bar-Natan, Finite Type Invariants, in Encyclopedia of Mathematical Physics, (J.-P. Francoise, G. L. Naber and Tsou S. T., eds.) Elsevier, Oxford, 2006 (vol. 2 p. 340).
  • S. Chmutov, S. Duzhin, and J. Mostovoy, Introduction to Vassiliev knot invariants, Cambridge University Press, Cambridge, 2012. MR 2962302, DOI 10.1017/CBO9781139107846
  • Joan S. Birman and Xiao-Song Lin, Knot polynomials and Vassiliev’s invariants, Invent. Math. 111 (1993), no. 2, 225–270. MR 1198809, DOI 10.1007/BF01231287
  • Predrag Cvitanović, Group theory, Princeton University Press, Princeton, NJ, 2008. Birdtracks, Lie’s, and exceptional groups. MR 2418111, DOI 10.1515/9781400837670
  • M. N. Gusarov, A new form of the Conway-Jones polynomial of oriented links, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 193 (1991), no. Geom. i Topol. 1, 4–9, 161 (Russian, with English summary). MR 1157140
  • M. Gusarov, On $n$-equivalence of knots and invariants of finite degree, Topology of manifolds and varieties, Adv. Soviet Math., vol. 18, Amer. Math. Soc., Providence, RI, 1994, pp. 173–192. MR 1296895, DOI 10.1007/bf01130282
  • Vaughan F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 1, 103–111. MR 766964, DOI 10.1090/S0273-0979-1985-15304-2
  • Maxim Kontsevich, Vassiliev’s knot invariants, I. M. Gel′fand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 137–150. MR 1237836
  • Maxim Kontsevich, Feynman diagrams and low-dimensional topology, First European Congress of Mathematics, Vol. II (Paris, 1992) Progr. Math., vol. 120, Birkhäuser, Basel, 1994, pp. 97–121. MR 1341841
  • Roger Penrose, Applications of negative dimensional tensors, Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969) Academic Press, London, 1971, pp. 221–244. MR 0281657
  • 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
  • V. A. Vassiliev, Cohomology of knot spaces, Theory of singularities and its applications, Adv. Soviet Math., vol. 1, Amer. Math. Soc., Providence, RI, 1990, pp. 23–69. MR 1089670
  • V. A. Vassiliev, Complements of discriminants of smooth maps: topology and applications, Translations of Mathematical Monographs, vol. 98, American Mathematical Society, Providence, RI, 1992. Translated from the Russian by B. Goldfarb. MR 1168473, DOI 10.1090/conm/478
  • Edward Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399. MR 990772

  • Review Information:

    Reviewer: Dror Bar-Natan
    Affiliation: University of Toronto, Canada
    Journal: Bull. Amer. Math. Soc. 50 (2013), 685-690
    Published electronically: April 17, 2013
    Additional Notes: Picture credits: Rope from “The Project Gutenberg eBook, Knots, Splices and Rope Work, by A. Hyatt Verrill”, Plane from NASA,
    TeX at This review was written while I was a guest at the Newton Institute, in Cambridge, UK. I wish to thank N. Bar-Natan, I. Halacheva, and P. Lee for comments and suggestions.
    Review copyright: © Copyright 2013 by the author under Creative Commons Attribution-NonCommercial 3.0 Unported License