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The $C$–polynomial of a knot

Stavros Garoufalidis and Xinyu Sun

Algebraic & Geometric Topology 6 (2006) 1623–1653
Bibliography
1 D Bar-Natan, KnotAtlas
2 D Bar-Natan, S Garoufalidis, On the Melvin–Morton–Rozansky conjecture, Invent. Math. 125 (1996) 103 MR1389962
3 D W Boyd, Mahler's measure and special values of $L$–functions, Experiment. Math. 7 (1998) 37 MR1618282
4 D Cooper, M Culler, H Gillet, D D Long, P B Shalen, Plane curves associated to character varieties of 3–manifolds, Invent. Math. 118 (1994) 47 MR1288467
5 M Culler, A table of $A$–polynomials
6 S Garoufalidis, On the characteristic and deformation varieties of a knot, from: "Proceedings of the Casson Fest", Geom. Topol. Monogr. 7 (2004) 291 MR2172488
7 S Garoufalidis, T T Q Lê, Asymptotics of the colored Jones function of a knot arXiv:math.GT/0508100
8 S Garoufalidis, T T Q Lê, The colored Jones function is $q$–holonomic, Geom. Topol. 9 (2005) 1253 MR2174266
9 S Garoufalidis, X Sun, The non-commutative $A$–polynomial of twist knots
10 K Habiro, On the quantum $\mathrm sl_2$ invariants of knots and integral homology spheres, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)", Geom. Topol. Monogr. 4 (2002) 55 MR2002603
11 J Hoste, P D Shanahan, Trace fields of twist knots, J. Knot Theory Ramifications 10 (2001) 625 MR1831680
12 J Hoste, P D Shanahan, A formula for the A-polynomial of twist knots, J. Knot Theory Ramifications 13 (2004) 193 MR2047468
13 V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. $(2)$ 126 (1987) 335 MR908150
14 F Kirwan, Complex algebraic curves, London Mathematical Society Student Texts 23, Cambridge University Press (1992) MR1159092
15 T H Koornwinder, On Zeilberger's algorithm and its $q$–analogue, J. Comput. Appl. Math. 48 (1993) 91 MR1246853
16 T T Q Lê, The Colored Jones Polynomial and the $A$–Polynomial of Two-Bridge Knots, Advances in Math. in press
17 G Masbaum, Skein-theoretical derivation of some formulas of Habiro, Algebr. Geom. Topol. 3 (2003) 537 MR1997328
18 P Paule, A Riese, The Paule/Schorn Implementation of Gosper's and Zeilberger's Algorithms, Mathematica software
19 P Paule, A Riese, qZeil, Mathematica software
20 P Paule, A Riese, A Mathematica $q$–analogue of Zeilberger's algorithm based on an algebraically motivated approach to $q$–hypergeometric telescoping, from: "Special functions, $q$–series and related topics (Toronto, ON, 1995)", Fields Inst. Commun. 14, Amer. Math. Soc. (1997) 179 MR1448687
21 M Petkovšek, H S Wilf, D Zeilberger, $A=B$, A K Peters Ltd. (1996) MR1379802
22 D Rolfsen, Knots and links, Publish or Perish (1976) MR0515288
23 V G Turaev, The Yang–Baxter equation and invariants of links, Invent. Math. 92 (1988) 527 MR939474
24 H S Wilf, D Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and “$q$”) multisum/integral identities, Invent. Math. 108 (1992) 575 MR1163239
25 D Zeilberger, Maple software
26 X Zhang, The $C$–polynomial of a knot, Topology Appl. 139 (2004) 185 MR2051104