Geometric & Functional Analysis GAFA

, Volume 6, Issue 2, pp 268–300 | Cite as

Invariants of three-dimensional manifolds

  • S. Gelfand
  • D. Kazhdan
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [CPr]
    V. Chari, A. Pressley, A Guide to Quantum Groups, Cambridge Univ. Press, Cambridge, 1994Google Scholar
  2. [DMi]
    P. Deligne, J. Milne, Tannakian categories, in Springer Lecture Notes Math. 900 (1982), 101–228.Google Scholar
  3. [DuJN]
    B. Durhuus, H. Jackobsen, R. Nest, A construction of topological quantum field theories from 6j-symbols, Nuclear Phys. B Proc. Suppl. 25A (1992), 109–121.Google Scholar
  4. [FG]
    G. Felder, O. Grandjean, On combinatorial three-manifold invariants, Preprint, 1992.Google Scholar
  5. [KS]
    M. Karowski, R. Schrader, A combinatorial approach to topological quantum field theories and invariants of graphs, Commun. Math. Phys. 151 (1993), 355–402.Google Scholar
  6. [Ke]
    T. Kerler, Mapping class group actions on quantum doubles, Preprint, 1993.Google Scholar
  7. [Ku]
    G. Kuperberg, Non-involutory Hopf algebras and 3-manifold invariants, Preprint 1994.Google Scholar
  8. [L]
    V. Lyubashenko, Ribbon categories as modular categories, Preprint, 1993.Google Scholar
  9. [M]
    S. Majid, Representations, duals and quantum doubles of monoidal categories, Rend. Circ. Mat. Palermo Suppl. 26 (1991), 197–206.Google Scholar
  10. [Pa]
    U. Pachner, Uber die bistellare Aquivalenz simplizialer Spharen und Polytope, Math. Z. 176 (1981), 565–576.Google Scholar
  11. [Po]
    M. Polyak, Graphical approach to the 3-manifold invariants of Turaev-Viro, J. Knot Theory Ramifications 1 (1992), 219–240.Google Scholar
  12. [RT1]
    N. Reshtikhin, V. Turaev, Ribbon graphs and their invariants from quantum groups Comm. Math. Phys. 127 (1990), 1–26.Google Scholar
  13. [RT2]
    N. Reshtikhin, V. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups Invent. Math. 103 (1991), 547–598.Google Scholar
  14. [Ro]
    J. Roberts, Skein theory and Turaev-Viro invariants, Preprint, 1993.Google Scholar
  15. [T1]
    V. Turaev, Topology of shadows, Preprint, 1991.Google Scholar
  16. [T2]
    V. Turaev, Quantum Invariants of Knot and 3-manifolds, Walter de Gruyter, Berlin, 1994.Google Scholar
  17. [TV]
    V. Turaev, O. Viro, State sum invariants of 3-manifolds and quantum 6j-symbols, Topology 31 (1992), 865–902.Google Scholar
  18. [W]
    K. Walker, On Witten's 3-manifold invariants, Preprint, 1991.Google Scholar

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • S. Gelfand
    • 1
  • D. Kazhdan
    • 2
  1. 1.American Mathematical SocietyProvidenceUSA
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA

Personalised recommendations