Refined quantum invariants for three-manifolds with structure

Blanchet, Christian

Banach Center Publications, Tome 43 (1998), p. 11-22 / Harvested from The Polish Digital Mathematics Library

Détail

Publié le : 1998-01-01

Zbl 0911.57011

EUDML-ID : urn:eudml:doc:208800

Bibliographie

[000] [At] M. F. Atiyah, Topological quantum field theories, Publ. Math. IHES 68 (1989) 175-186.

[001] [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. | Zbl 0771.57004

[002] [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). | Zbl 0839.57013

[003] [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. | Zbl 0887.57009

[004] [Bl1] C. Blanchet, Invariants on three-manifolds with spin structure, Comm. Math. Helv. 67 (1992), 406-427. | Zbl 0771.57005

[005] [Bl2] C. Blanchet, On spin type structures related with quantum invariants, in preparation.

[006] [BM] C. Blanchet and G. Masbaum, Topological Quantum Field Theories for surfaces with spin structure, Duke Math. Journal 82 No 2 (1996), 229-267. | Zbl 0854.57025

[007] [FR] R. Fenn and C. Rourke, On Kirby calculus of links, Topology 18 (1979) 1-15. | Zbl 0413.57006

[008] [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. | Zbl 0772.57022

[009] [Jo] V. Jones, A polynomial invariant for knots via Von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103-111. | Zbl 0564.57006

[010] [Ka] L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395-407. | Zbl 0622.57004

[011] [Ki] R. Kirby, A calculus of framed links in $S^3$, Invent. Math. 45 (1978), 35-56. | Zbl 0377.55001

[012] [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. | Zbl 0745.57006

[013] [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.

[014] [Li1] W. B. R. Lickorish, Three-manifold invariants and the Temperley-Lieb algebra, Math. Ann. 290 (1991), 657-670. | Zbl 0739.57004

[015] [Li2] W. B. R. Lickorish, Calculations with the Temperley-Lieb algebra, Comm. Math. Helv. 67 (1992), 571-591. | Zbl 0779.57008

[016] [Li3] W. B. R. Lickorish, The skein method for 3-manifolds invariants, J. Knot. Th. Ram. 2 (1993), 171-194. | Zbl 0793.57003

[017] [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). | Zbl 0966.57016

[018] [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.

[019] [ML] S. Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer-Verlag (1971).

[020] [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. | Zbl 0776.57009

[021] [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). | Zbl 0855.57014

[022] [Mu] H. Murakami, Quantum invariants for 3-manifolds, Proc. of the 3rd Korea-Japan School of knots and links (to appear).

[023] [OY] T. Ohtsuki and S. Yamada, Quantum SU(3) invariants via linear skein theory, J. Knot Theory Ram. 6 (1997), 373-404. | Zbl 0949.57011

[024] [P] J. Przytycki, Skein modules of 3-manifolds, Bull. Ac. Pol. Math. 39(1-2) (1991), 91-100. | Zbl 0762.57013

[025] [RT] N. Reshetikhin and V. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), 547-598. | Zbl 0725.57007

[026] [St] R. E. Stong, Notes on cobordism theory, Princeton Univ. Press (1968).

[027] [Tu1] V. G. Turaev, State sum models in low-dimensional topology, Proc. ICM Kyoto 1990, vol I, 689-698. | Zbl 0744.57007

[028] [Tu2] V. G. Turaev, Quantum invariants of knots and 3-manifolds, De Gruyter Studies in Math. 18 (1994).

[029] [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.

[030] [Vo] P. Vogel, Les invariants récents des variétés de dimension 3, Séminaire Bourbaki 799 (1995).

[031] [Wi] E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399. | Zbl 0667.57005

[032] [Yo] Y. Yokota, Skeins and quantum SU(N) invariants of 3-manifolds, Math. Ann. 307 (1997), 109-138. | Zbl 0953.57009