Invariants of three-manifolds, unitary representations of the mapping class group, and numerical calculations

Experimental Mathematics

Volumn 6, Issue 4, 1997, Pages 317-352

  Karowski, Michael ^a   Schrader, Robert ^a   Vogt, Elmar ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031283969     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.1997.10504619     Document Type: Article

References (43)

1. M. Atiyah, "On framings of 3-manifolds", Topology 29:1 (1990), 1-7.
2. A. Beliakova and B. Durhuus, "Topological quantum field theory and invariants of graphs for quantum groups", Comm. Math. Phys. 167:2 (1995), 395-429.
3. B. Durhuus, "A discrete approach to topological quantum field theories", J. Geom. Phys. 11:1-4 (1993), 155-180.
4. B. Durhuus, H. P. Jakobsen, and R. Nest, "Topological quantum field theories from generalized 6j-symbols", Rev. Math. Phys. 5:1 (1993), 1-67.
5. D. S. Freed and R. E. Gompf, "Computer calculation of Witten's 3-manifold invariant", Comm. Math. Phys. 141:1 (1991),79-117.
6. J. Frohlich and C. King, "The Chern-Simons theory and knot polynomials", Comm. Math. Phys. 126:1 (1989), 167-199.
7. D. Gepner and E. Witten, "String theory on group manifolds", Nuclear Phys. B 278:3 (1986), 493-549.
8. C. Haase, Reidemeister- Torsion und Chirorgien an der Achterschlinge, Diplomarbeit, Freie Universitat Berlin, February 1997.
9. R. J. Harrington, Witten's SU(2) invariant for a family of hyperbolic 3-manifolds, Ph.D. thesis, University of Texas, Austin, TX, December 1996.
10. P. Heegaard, "Sur l'Analysis situs", Bull. Soc. Math. France 44 (1916), 161-242.
11. L. C. Jeffrey, "Chern-Simons-Witten invariants of lens spaces and torus bundles, and thesemiclassical approximation", Comm. Math. Phys. 147:3 (1992), 563-604.
12. V. F. R. Jones, "A polynomial invariant for knots via von Neumann algebras", Bull. Amer. Math. Soc. (N.S.) 12:1 (1985), 103-111.
13. V. F. R. Jones, "Heeke algebra representations of braid groups and link polynomials", Ann. of Math. (2) 126:2 (1987), 335-388.
14. M. Karowski, "Topological quantum field theories in terms of coloured graphs associated to quantum groups", pp. 118 in Group Theoretical Methods in Physics (Salamanca, 1992), vol. 2, edited by M. A. del Olmo et al., Ciemat, Madrid, 1992.
15. M. Karowski and R. Schrader, "A combinatorial approach to topological quantum field theories and invariants of graphs", Comm. Math. Phys. 151:2 (1993), 355-02.
16. M. Karowski, W. Miiller, and R. Schrader, "State sum invariants of compact 3manifolds with boundary and 6j-symbols", J. Phys. A 25:18 (1992), 4847-4860.
17. R. Kirby and P. Melvin, "The 3-manifold invariants of Witten and ReshetikhinTuraev for sl(2, C)", Invent. Math. 105:3 (1991), 473-545.
18. A. N. Kirillov and N. Y. Reshetikhin, "Representation of the Algebra Uq (sl (2)), q-orthogonal Polynomials and invariants of links", in New developments in the theory of knots, edited by T. Kohno, Advances series in Mathematical Physics 11, World Scientific, Singapore, 1989.
19. P. A. Kirk and E. P. Klassen, "Chern-Simons invariants of 3-manifolds and representation spaces of not groups", Math. Ann. 287:2 (1990), 343-367.
20. T. Kohno, "Topological invariants for 3-manifolds using representations of mapping class groups, r', Topology 31:2 (1992), 203-230.
21. T. Kohno, "Topological invariants for 3-manifolds using representations of mapping class groups, II: Estimating tunnel number of knots", pp. 193-217 in Mathematical aspects of conformal and topological field theories and quantum groups (South Hadley, MA, 1992), Contemp. Math. 175, Amer. Math. Soc., Providence, Rl, 1994.
22. R. J. Lawrence, "Asymptotic expansions of Witten-Reshetikhin-Turaev invariants for some simple 3-manifolds", J. Math. Phys. 36:11 (1995), 6106-6129.
23. G. Moore and N. Seiberg, "Classical and quantum conformal field theory", Comm. Math. Phys. 123:2 (1989), 177-254.
24. H. Murakami, "Quantum SO(3)invariants dominate the SU(2)-invariant of Casson and Walker", Math. Proc. Cambridge Philos. Soc. 117:2 (1995), 237-249.
25. T. Ohtsuki, "A polynomial invariant of integral homology 3-spheres", Math. Proc. Cambridge Philos. Soc. 117:1 (1995), 83-112.
26. T. Ohtsuki, "A polynomial invariant of rational homology 3-spheres", Invent. Math. 123:2 (1996), 241-257.
27. K. Osterwalder and R. Schrader, "Axioms for Euclidean Green's functions", Comm. Math. Phys. 31 (1973), 83-112.
28. K. Osterwalder and R. Schrader, "Axioms for Euclidean Green's functions. II", Comm. Math. Phys. 42 (1975), 281-305.
29. N. Y. Reshetikhin and V. G. Turaev, "Ribbon graphs and their invariants derived from quantum groups", Comm. Math. Phys. 127:1 (1990), 1-26.
30. N. Reshetikhin and V. G. Turaev, "Invariants of 3-manifolds via link polynomials and quantum groups", Invent. Math. 103:3 (1991), 547-597.
31. L. Rozansky, "A large k asymptotics of Witten's invariant of Seifert manifolds", Comm. Math. Phys. 171:2 (1995), 279-322.
32. L. Rozansky, "The trivial connection contribution to Witten's invariant and finite type invariants of rational homology spheres", Comm. Math. Phys. 183:1 (1997), 23-54.
33. E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966.
34. V. Turaev, "Quantum invariants of 3manifolds and a glimpse of shadow topology", C. R. Acad. Sci. Paris Sere I Math. 313:6 (1991), 395-398.
35. V. G. Turaev, "State sums in lowdimensional topology", pp. 689-698 in Proc. International Congress of Mathematicians (Kyoto, 1990), vol. 1, 1991.
36. V. G. Turaev, "Topology of shadows", preprint, 1991.
37. V. G. Turaev, "Quantum invariants of 3-manifolds I and II", preprint 1992/015, Universite de Strasbourg, 1992.
38. V. Turaev, "Quantum invariants of links and 3-valent graphs in 3-manifolds", Inst. Hautes Etudes Sci. Publ. Math. 77 (1993), 121-171.
39. V. G. Turaev and O. Y. Viro, "State sum invariants of 3-manifolds and quantum 6j-symbols", Topology 31:4 (1992), 865-902.
40. B. Wajnryb, "A simple presentation for the mapping class group of an orientable surface", Israel J. Math. 45:2-3 (1983),157-174.
41. K. Walker, "On Witten's three-manifold invariants", preprint, 1991.
42. H. Wenzl, "Braids and invariants of 3manifolds", Invent. Math. 114:2 (1993), 235-275.
43. E. Witten, "Quantum field theory and the Jones polynomial", Comm. Math. Phys. 121:3 (1989), 351-399.