Refined quantum invariants for three-manifolds with structure

Christian Blanchet

Banach Center Publications (1998)

  • Volume: 42, Issue: 1, page 11-22
  • ISSN: 0137-6934

How to cite


Blanchet, Christian. "Refined quantum invariants for three-manifolds with structure." Banach Center Publications 42.1 (1998): 11-22. <>.

author = {Blanchet, Christian},
journal = {Banach Center Publications},
keywords = {3-manifolds; skein theory; quantum invariants; spin structures; TQFT},
language = {eng},
number = {1},
pages = {11-22},
title = {Refined quantum invariants for three-manifolds with structure},
url = {},
volume = {42},
year = {1998},

AU - Blanchet, Christian
TI - Refined quantum invariants for three-manifolds with structure
JO - Banach Center Publications
PY - 1998
VL - 42
IS - 1
SP - 11
EP - 22
LA - eng
KW - 3-manifolds; skein theory; quantum invariants; spin structures; TQFT
UR -
ER -


  1. [At] M. F. Atiyah, Topological quantum field theories, Publ. Math. IHES 68 (1989) 175-186. 
  2. [BHMV1] C. Blanchet, N. Habegger, G. Masbaum and P. Vogel, Three-manifold invariants derived from the Kauffman bracket, Topology 31 No 4 (1992), 685-699. Zbl0771.57004
  3. [BHMV2] C. Blanchet, N. Habegger, G. Masbaum and P. Vogel, Remarks on the Three-manifold Invariants θ p , in ’Operator Algebras, Mathematical Physics, and Low Dimensional Topology’ (R. Herman, B. Tanbay, Ed.), A.K.Peters Research Notes in Mathematics Vol 5, 39-59 (1993). Zbl0839.57013
  4. [BHMV3] C. Blanchet, N. Habegger, G. Masbaum and P. Vogel, Topological Quantum Field Theories derived from the Kauffman bracket, Topology 34 No 4 (1995), 883-927. Zbl0887.57009
  5. [Bl1] C. Blanchet, Invariants on three-manifolds with spin structure, Comm. Math. Helv. 67 (1992), 406-427. Zbl0771.57005
  6. [Bl2] C. Blanchet, On spin type structures related with quantum invariants, in preparation. 
  7. [BM] C. Blanchet and G. Masbaum, Topological Quantum Field Theories for surfaces with spin structure, Duke Math. Journal 82 No 2 (1996), 229-267. Zbl0854.57025
  8. [FR] R. Fenn and C. Rourke, On Kirby calculus of links, Topology 18 (1979) 1-15. Zbl0413.57006
  9. [HP] J. Hoste and J. Przytycki, A survey of skein modules of 3-manifolds, in 'Knots 90', Proceedings of the International Conference on Knot Theory and Related Topics, Osaka (Japan), August 15-19, 1990 (A. Kawauchi Ed.), Walter de Gruyter (1992), 363-379. Zbl0772.57022
  10. [Jo] V. Jones, A polynomial invariant for knots via Von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103-111. Zbl0564.57006
  11. [Ka] L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395-407. Zbl0622.57004
  12. [Ki] R. Kirby, A calculus of framed links in S 3 , Invent. Math. 45 (1978), 35-56. Zbl0377.55001
  13. [KM] R. Kirby and P. Melvin, The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2,C), Inv. Math. 105 (1991), 473-545. Zbl0745.57006
  14. [KT] T. Khono and T. Takata, Symmetry of Witten 3-manifold invariants for sl(n,C), Journal of Knot Theory Ram. Vol. 2 No 2 (1993) 149-169. 
  15. [Li1] W. B. R. Lickorish, Three-manifold invariants and the Temperley-Lieb algebra, Math. Ann. 290 (1991), 657-670. Zbl0739.57004
  16. [Li2] W. B. R. Lickorish, Calculations with the Temperley-Lieb algebra, Comm. Math. Helv. 67 (1992), 571-591. Zbl0779.57008
  17. [Li3] W. B. R. Lickorish, The skein method for 3-manifolds invariants, J. Knot. Th. Ram. 2 (1993), 171-194. Zbl0793.57003
  18. [MA] H. R. Morton and A. K. Aiston, Young diagrams, the Homfly skein of the annulus and unitary invariants, Proceedings of Knots 96, Tokyo (to appear). Zbl0966.57016
  19. [Mo] H. R. Morton, Invariants of links and 3-manifolds from skein theory and from quantum groups, In 'Topics in knot theory', the Proceedings of the NATO Summer Institute in Arzurum, NATO ASI Series C 399 (M. Bozhüyük Ed.), Kluwer (1993), 107-156. 
  20. [ML] S. Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer-Verlag (1971). 
  21. [MOO] H. Murakami, T. Othsuki and M. Okada, Invariants of three-manifolds derived from linking matrices of framed links, Osaka J. Math. 29 (1992), 545-572. Zbl0776.57009
  22. [MPR] J. Mattes, M. Polyak and N. Reshetikhin, On invariants of 3-manifolds derived from abelians groups, in 'Quantum Topology' (L. Kaufmann, R. Baadhio Ed.), World Scientific (1993). Zbl0855.57014
  23. [Mu] H. Murakami, Quantum invariants for 3-manifolds, Proc. of the 3rd Korea-Japan School of knots and links (to appear). 
  24. [OY] T. Ohtsuki and S. Yamada, Quantum SU(3) invariants via linear skein theory, J. Knot Theory Ram. 6 (1997), 373-404. Zbl0949.57011
  25. [P] J. Przytycki, Skein modules of 3-manifolds, Bull. Ac. Pol. Math. 39(1-2) (1991), 91-100. Zbl0762.57013
  26. [RT] N. Reshetikhin and V. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-598. Zbl0725.57007
  27. [St] R. E. Stong, Notes on cobordism theory, Princeton Univ. Press (1968). 
  28. [Tu1] V. G. Turaev, State sum models in low-dimensional topology, Proc. ICM Kyoto 1990, vol I, 689-698. Zbl0744.57007
  29. [Tu2] V. G. Turaev, Quantum invariants of knots and 3-manifolds, De Gruyter Studies in Math. 18 (1994). 
  30. [TW] V. G. Turaev and H. Wenzl Quantum invariants of 3-manifolds associated with classical simple Lie algebras, Int. Journal of Math. Vol. 4 No 2 (1993) 323-358. 
  31. [Vo] P. Vogel, Les invariants récents des variétés de dimension 3, Séminaire Bourbaki 799 (1995). 
  32. [Wi] E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. Zbl0667.57005
  33. [Yo] Y. Yokota, Skeins and quantum SU(N) invariants of 3-manifolds, Math. Ann. 307 (1997), 109-138. Zbl0953.57009

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