Algebraic & Geometric Topology Volume 4, issue 2 (2004)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Non-triviality of the $A$–polynomial for knots in $S^3$

Nathan M Dunfield and Stavros Garoufalidis

Algebraic & Geometric Topology 4 (2004) 1145–1153

DOI: 10.2140/agt.2004.4.1145

Bibliography

1	S Boyer, X Zhang, Every nontrivial knot in $S^3$ has nontrivial $A$–polynomial, Proc. Amer. Math. Soc. 133 (2005) 2813 MR2146231
2	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
3	D Cooper, D D Long, Remarks on the $A$–polynomial of a knot, J. Knot Theory Ramifications 5 (1996) 609 MR1414090
4	M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. $(2)$ 117 (1983) 109 MR683804
5	N M Dunfield, Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds, Invent. Math. 136 (1999) 623 MR1695208
6	S Francaviglia, Hyperbolic volume of representations of fundamental groups of cusped 3–manifolds, Int. Math. Res. Not. (2004) 425 MR2040346
7	S Garoufalidis, T T Q Lê, The colored Jones function is $q$–holonomic, Geom. Topol. 9 (2005) 1253 MR2174266
8	S Garoufalidis, On the characteristic and deformation varieties of a knot, from: "Proceedings of the Casson Fest", Geom. Topol. Monogr. 7, Geom. Topol. Publ., Coventry (2004) 291 MR2172488
9	A E Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math. 99 (1982) 373 MR658066
10	P B Kronheimer, T S Mrowka, Dehn surgery, the fundamental group and SU$(2)$, Math. Res. Lett. 11 (2004) 741 MR2106239
11	L Ng, Framed knot contact homology, Duke Math. J. 141 (2008) 365 MR2376818
12	P B Shalen, Representations of 3–manifold groups, from: "Handbook of geometric topology", North-Holland (2002) 955 MR1886685
13	W Thurston, The geometry and topology of 3–manifolds, lecture notes, MSRI (1979)