Volume 17, issue 1 (2017)

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Detection of knots and a cabling formula for $A$–polynomials

Yi Ni and Xingru Zhang

Algebraic & Geometric Topology 17 (2017) 65–109
Bibliography
1 K L Baker, Closed essential surfaces in the complements of large volume Berge knots, preprint (2005) arXiv:math/0509082
2 J Berge, Some knots with surgeries yielding lens spaces, unpublished draft
3 S Boyer, X Zhang, Cyclic surgery and boundary slopes, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 62 MR1470721
4 S Boyer, X Zhang, On Culler–Shalen seminorms and Dehn filling, Ann. of Math. 148 (1998) 737 MR1670053
5 S Boyer, X Zhang, A proof of the finite filling conjecture, J. Differential Geom. 59 (2001) 87 MR1909249
6 S Boyer, X Zhang, Every nontrivial knot in S3 has nontrivial A–polynomial, Proc. Amer. Math. Soc. 133 (2005) 2813 MR2146231
7 G Burde, H Zieschang, Knots, 5, Walter de Gruyter (2003) MR1959408
8 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
9 M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. 125 (1987) 237 MR881270
10 M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. 117 (1983) 109 MR683804
11 N M Dunfield, S Garoufalidis, Non-triviality of the A–polynomial for knots in S3, Algebr. Geom. Topol. 4 (2004) 1145 MR2113900
12 M Eudave-Muñoz, Non-hyperbolic manifolds obtained by Dehn surgery on hyperbolic knots, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470720
13 M Eudave-Muñoz, On hyperbolic knots with Seifert fibered Dehn surgeries, Topology Appl. 121 (2002) 119 MR1903687
14 P Ghiggini, Knot Floer homology detects genus-one fibred knots, Amer. J. Math. 130 (2008) 1151 MR2450204
15 C M Gordon, Dehn surgery and satellite knots, Trans. Amer. Math. Soc. 275 (1983) 687 MR682725
16 C M Gordon, J Luecke, Only integral Dehn surgeries can yield reducible manifolds, Math. Proc. Cambridge Philos. Soc. 102 (1987) 97 MR886439
17 C M Gordon, J Luecke, Non-integral toroidal Dehn surgeries, Comm. Anal. Geom. 12 (2004) 417 MR2074884
18 M Hedden, On knot Floer homology and cabling, II, Int. Math. Res. Not. 2009 (2009) 2248 MR2511910
19 M Hirasawa, K Murasugi, D S Silver, When does a satellite knot fiber?, Hiroshima Math. J. 38 (2008) 411 MR2477750
20 P B Kronheimer, T S Mrowka, Dehn surgery, the fundamental group and SU(2), Math. Res. Lett. 11 (2004) 741 MR2106239
21 P B Kronheimer, T S Mrowka, Khovanov homology is an unknot-detector, Publ. Math. Inst. Hautes Études Sci. 113 (2011) 97 MR2805599
22 S Lang, Algebra, Addison Wesley (1993)
23 Y Ni, Knot Floer homology detects fibred knots, Invent. Math. 170 (2007) 577 MR2357503
24 P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311 MR2023281
25 P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
26 P D Shanahan, Cyclic Dehn surgery and the A–polynomial, Topology Appl. 108 (2000) 7 MR1783421
27 T Soma, On preimage knots in S3, Proc. Amer. Math. Soc. 100 (1987) 589 MR891169
28 X Zhang, The C–polynomial of a knot, Topology Appl. 139 (2004) 185 MR2051104