Quantum Groups pp 363-366 | Cite as

Quantum invariants of 3-manifold and a glimpse of shadow topology

  • Vladimir Turaev
III. Quantum Groups, Low-Dimensional Topology And Link Invariants
Part of the Lecture Notes in Mathematics book series (LNM, volume 1510)


The paper announces explicit formulas relating two different approaches to constructing quantum invariants of 3-manifolds (see [1], [2]). A new formula for the linking number of classical knots is presented which enables one to extend the first of these approaches to ghost 3-manifold over ℂ.


Hopf Algebra Quantum Group Tensor Category Reidemeister Move Link Diagram 
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  1. [1]
    N.Y. Reshetikhin, V.G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    V.Turaev and O.Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology (to appear).Google Scholar
  3. [3]
    V.Turaev, Quantum invariants of links and 3-valent graphs in 3-manifolds, Preprint (1990).Google Scholar
  4. [4]
    V.Turaev, State sum models in low-dimensional topology, Proc. ICM-90, Kyoto (to appear).Google Scholar
  5. [5]
    V.Turaev, Shadow links and IRF-models of statistical mechanics, Publ. Inst. Rech. Math. Av. (1990), Strasbourg; J. Diff. Geom. (to appear).Google Scholar
  6. [6]
    V.Turaev, Topology of shadows, In preparation.Google Scholar
  7. [7]
    K.Walker, On Witten's 3-manifolds invariants, Preprint (November 1990), Strasbourg.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Vladimir Turaev
    • 1
  1. 1.Leningrad Branch of Steklov Mathematical Institute and Université Louis PasteurStrasbourg

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