Asymptotic Expansions of Witten-Reshetikhin-Turaev Invariants for Some Simple $3$-Manifolds

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1. [1] E. Witten, 'Quantum Field Theory and the Jones Polynomial', Commun. Math. Phys.121 (1989) p. 351-399. Zbl0667.57005MR990772
2. [2] M. F. Atiyah, 'The Geometry and Physics of Knots', Lezione LinceeCambridge University Press (1990). Zbl0729.57002MR1027859
3. [3] S. Axelrod, I. M. Singer, 'Chern-Simons perturbation theory', Proc. XXthInt. Conf. Diff. Geom. Methods in Th. Phys., World Scientific (1991) p. 3-45. Zbl0813.53051MR1225107
4. [4] S. Axelrod, I. M. Singer, 'Chern-Simons perturbation theory II', J. Diff. Geom.39 (1994) p. 173-213. Zbl0827.53057MR1258919
5. [5] J. C. Baez, 'Link invariants of finite type and perturabation theory', Lett. Math. Phys.26 (1992) p. 43-51. Zbl0792.57002MR1193625
6. [6] D. Bar-Natan, 'Perturbative Chern-Simons Theory', preprint 1994. Zbl0861.57009MR1361082
7. [7] L. Rozansky, 'Witten's invariant of 3-dimensional manifolds: Loop expansion and surgery calculus', preprint (1993). Zbl1149.58307MR1364193
8. [8] L. Rozansky, 'A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds I, II', preprint (1994). Zbl0872.57011MR1552634
9. [9] M. F. Atiyah, 'Topological quantum field theory', Publ. Math. IHES68 (1989) p. 175-186. Zbl0692.53053MR1260745
10. [10] N. Yu. Reshetikhin, V. G. Turaev, 'Invariants of 3-manifolds via link polynomials and quantum groups', Invent. Math.103 (1991) p. 547-597. Zbl0725.57007MR1091619
11. [11] L. H. Kauffman, S. Lins, 'Temperley-Lieb recoupling theory and invariants of 3-manifolds', Princeton University Press (1994). Zbl0821.57003MR1280463
12. [12] D. S. Freed, R. E. Gompf, 'Computer Calculation of Witten's 3-Manifold Invariant', Commun. Math. Phys.141 (1991) p. 79-117. Zbl0739.53065MR1133261
13. [13] L. C. Jeffrey, 'Chern-Simons-Witten Invariants of Lens Spaces and Torus Bundles, and the Semiclassical Approximation', Commun. Math. Phys.147 (1992) p. 563-604. Zbl0755.53054MR1175494
14. [14] L. H. Kauffman, S. Lins, 'Computing Turaev-Viro Invariants for 3-manifolds', Manuscripta Math.72 (1991) p. 81-94. Zbl0725.57008MR1107454
15. [15] R. Kirby, P. Melvin, 'Evaluations of the 3-Manifold invariants of Witten and Reshetikhin-Turaev for sl(2,C)' , Geometry of lowdimensional manifolds, Cambridge Univ. Press, Lond. Math. Soc.Lect. Note Ser. 151 (1990) p. 101-114. Zbl0756.57006MR1171911
16. [16] R. Kirby, P. Melvin, 'The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2,C)', Invent. Math.105 (1991) p. 473-545. Zbl0745.57006MR1117149
17. [17] J. R. Neil, 'Combinatorial calculation of the various normalizations of the Witten invariants for 3-manifolds', J. Knot Th. Ram.1 (1992) p. 407-449. Zbl0766.57011MR1194996
18. [18] H. Murakami, 'Quantum SU(2)-invariants dominate Casson's SU(2)-invariant', Math. Proc. Camb. Phil. Soc.115 (1993) p. 253-281. Zbl0832.57005MR1277059
19. [19] T. Ohtsuki, 'A polynomial invariant of integral homology 3-spheres', Math. Proc. Camb. Phil. Soc. (to appear). Zbl0843.57019MR1297897
20. [20] H. Murakami, 'Quantum SO(3)-invariants dominate the SU(2)-invariant of Casson and Walker', preprint (1993). Zbl0854.57016MR1307078
21. [21] K. Walker, 'An Extension of Casson's Invariant', Annals of Mathematical Studies126Princeton University Press (1992). Zbl0752.57011MR1154798
22. [22] P. Cartier, 'An Introduction to Zeta Functions', From Number Theory to Physics, eds. M. Waldschmidt, P. Moussa, J.-M. Luck, C. Itzykson, Springer Verlag (1992) p. 1-63. Zbl0790.11061MR1221100
23. [23] D. Bar-Natan, 'On the Vassiliev knot invariants', Topology (to appear). Zbl0898.57001MR1318886
24. [24] S. Garoufalidis, 'On finite type 3-manifold invariants I', preprint (1995). Zbl0889.57015MR1406715
25. [25] T. Ohtsuki, 'Finite type invariants of integral homology 3-spheres', preprint (1994). Zbl0942.57009MR1373813
26. [26] V. G. Turaev, O. Ya. Viro, 'State Sum Invariants of 3-manifolds and quantum 6j-symbols' Topology31 (1992) p. 865-902. Zbl0779.57009MR1191386