The colored Jones polynomial and the A-polynomial of Knots

Advances in Mathematics

Volumn 207, Issue 2, 2006, Pages 782-804

  Lê, Thang T Q ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

A polynomial; AJ conjecture; Jones polynomial; Kauffman bracket skein module; Two bridge knots

Indexed keywords

EID: 33749065744     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2006.01.006     Document Type: Article

References (27)

1. Bar-Natan D., and Garoufalidis S. On the Melvin-Morton-Rozansky conjecture. Invent. Math. 125 1 (1996) 103-133
2. Burde G., and Zieschang H. Knots. de Gruyter Stud. Math. vol. 5 (2003), de Gruyter, Berlin
3. Bullock D. The (2, ∞)-skein module of the complement of a (2, 2 p + 1) torus knot. J. Knot Theory Ramifications 4 4 (1995) 619-632
4. Bullock D. Rings of SL2C-characters and the Kauffman bracket skein module. Comment. Math. Helv. 72 4 (1997) 521-542
5. Bullock D., and Lo Faro W. The Kauffman bracket skein module of a twist knot exterior. Algebr. Geom. Topol. 5 (2005) 107-118 (electronic)
6. Cooper D., and Long D. Representation theory and the A-polynomial of a knot. Chaos Solitons Fractals 9 4/5 (1998) 749-763
7. Cooper D., Culler M., Gillett H., Long D.D., and Shalen P.B. Plane curves associated to character varieties of 3-manifolds. Invent. Math. 118 (1994) 47-84
8. Culler M., and Shalen P.B. Varieties of group representations and splittings of 3-manifolds. Ann. of Math. (2) 117 1 (1983) 109-146
9. Frohman C., and Gelca R. Skein modules and the noncommutative torus. Trans. Amer. Math. Soc. 352 10 (2000) 4877-4888
10. Frohman C., Gelca R., and Lofaro W. The A-polynomial from the noncommutative viewpoint. Trans. Amer. Math. Soc. 354 2 (2002) 735-747
11. Garoufalidis S. On the characteristic and deformation varieties of a knot. Proceedings of the Casson Fest. Geom. Topol. Monogr. vol. 7 (2004), Geom. Topol. Publ., Coventry 291-309 (electronic)
12. Garoufalidis S., and Lê T.T.Q. The colored Jones function is q-holonomic. Geom. Topol. 9 (2005) 1253-1293 (electronic)
13. Gelca R. On the relation between the A-polynomial and the Jones polynomial. Proc. Amer. Math. Soc. 130 4 (2002) 1235-1241 (electronic)
14. Hoste J., and Shanahan P. Commensurability classes of twist knots. J. Knot Theory Ramifications 14 1 (2005) 91-100
15. Hikami K. Difference equation of the colored Jones polynomial for torus knot. Internat. J. Math. 15 9 (2004) 959-965
16. Jones V.F.R. Polynomial invariants of knots via von Neumann algebras. Bull. Amer. Math. Soc. 12 (1985) 103-111
17. Kauffman L. States models and the Jones polynomial. Topology 26 (1987) 395-407
18. Lê T.T.Q. Varieties of representations and their subvarieties of cohomology jumps for knot groups. Mat. Sb. 184 2 (1993) 57-82 (in Russian); translation in:
19. Lê T.T.Q. Varieties of representations and their subvarieties of cohomology jumps for knot groups. Russian Acad. Sci. Sb. Math. 78 1 (1994) 187-209
20. T.T.Q. Lê, On the skein modules and the A-polynomial of two-bridge knots, submitted for publication
21. Lubotzky A., and Magid A. Varieties of representations of finitely generated groups. Mem. Amer. Math. Soc. 336 (1985) 1-117
22. Lickorish W.B.R. An Introduction to Knot Theory. Grad. Texts in Math. vol. 175 (1997), Springer
23. Melvin P.M., and Morton H.R. The coloured Jones function. Comm. Math. Phys. 169 3 (1995) 501-520
24. Przytycki J. Fundamentals of Kauffman bracket skein modules. Kobe J. Math. 16 (1999) 45-66
25. 2 (C)-character varieties. Topology 39 (2000) 115-148
26. Takata T. The colored Jones polynomial and the A-polynomial for twist knots. preprint. math.GT/0401068
27. Turaev V.G. Quantum Invariants of Knots and 3-Manifolds. de Gruyter Stud. Math. vol. 18 (1994), de Gruyter, Berlin