Volume 8, issue 2 (2008)

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Commensurability classes of $2$–bridge knot complements

Alan W Reid and Genevieve S Walsh

Algebraic & Geometric Topology 8 (2008) 1031–1057
Bibliography
1 I R Aitchison, J H Rubinstein, Combinatorial cubings, cusps, and the dodecahedral knots, from: "Topology '90 (Columbus, OH, 1990)", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 17 MR1184399
2 J Berge, Some knots with surgeries yielding lens spaces, to appear in the proceedings of the Cassonfest
3 M Boileau, S Boyer, G S Walsh, On commensurability of knot complements, preprint available at http://www.tufts.edu/ gwalsh01/
4 S Boyer, X Zhang, Finite Dehn surgery on knots, J. Amer. Math. Soc. 9 (1996) 1005 MR1333293
5 M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. $(2)$ 125 (1987) 237 MR881270
6 W D Dunbar, Hierarchies for $3$–orbifolds, Topology Appl. 29 (1988) 267 MR953958
7 F González-Acuña, W C Whitten, Imbeddings of three-manifold groups, Mem. Amer. Math. Soc. 99 (1992) MR1117167
8 O Goodman, D Heard, C Hodgson, Commensurators of cusped hyperbolic manifolds arXiv:0801.4815
9 C M Gordon, Dehn filling: a survey, from: "Knot theory (Warsaw, 1995)", Banach Center Publ. 42, Polish Acad. Sci. (1998) 129 MR1634453
10 J Hoste, P D Shanahan, Trace fields of twist knots, J. Knot Theory Ramifications 10 (2001) 625 MR1831680
11 H Koch, Number theory, Graduate Studies in Math. 24, Amer. Math. Soc. (2000) MR1760632
12 M L Macasieb, T W Mattman, Commensurability classes of $(-2,3,n)$ pretzel knot complements arXiv:0804.0112
13 C Maclachlan, A W Reid, The arithmetic of hyperbolic $3$–manifolds, Graduate Texts in Math. 219, Springer (2003) MR1937957
14 G A Margulis, Discrete subgroups and ergodic theory, from: "Number theory, trace formulas and discrete groups (Oslo, 1987)", Academic Press (1989) 377 MR993328
15 J Milnor, Groups which act on $S^n$ without fixed points, Amer. J. Math. 79 (1957) 623 MR0090056
16 W D Neumann, Commensurability and virtual fibration for graph manifolds, Topology 36 (1997) 355 MR1415593
17 W D Neumann, A W Reid, Arithmetic of hyperbolic manifolds, from: "Topology '90 (Columbus, OH, 1990)", Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 273 MR1184416
18 P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
19 A W Reid, A note on trace-fields of Kleinian groups, Bull. London Math. Soc. 22 (1990) 349 MR1058310
20 A W Reid, Arithmeticity of knot complements, J. London Math. Soc. $(2)$ 43 (1991) 171 MR1099096
21 R Riley, Parabolic representations of knot groups. I, Proc. London Math. Soc. $(3)$ 24 (1972) 217 MR0300267
22 R Riley, Seven excellent knots, from: "Low-dimensional topology (Bangor, 1979)", London Math. Soc. Lecture Note Ser. 48, Cambridge Univ. Press (1982) 81 MR662430
23 R Riley, Parabolic representations and symmetries of the knot $9_{32}$, from: "Computers in geometry and topology (Chicago, IL, 1986)", Lecture Notes in Pure and Appl. Math. 114, Dekker (1989) 297 MR988702
24 M Sakuma, The geometries of spherical Montesinos links, Kobe J. Math. 7 (1990) 167 MR1096689
25 R E Schwartz, The quasi-isometry classification of rank one lattices, Inst. Hautes Études Sci. Publ. Math. 82 (1995) 133 MR1383215
26 M Suzuki, Group theory. I, Grundlehren series 247, Springer (1982) MR648772
27 M o Takahashi, Two-bridge knots have property $\mathrm{P}$, Mem. Amer. Math. Soc. 29 (1981) MR597092
28 S C Wang, Y Q Wu, Any knot complement covers at most one knot complement, Pacific J. Math. 158 (1993) 387 MR1206445
29 S C Wang, Q Zhou, Symmetry of knots and cyclic surgery, Trans. Amer. Math. Soc. 330 (1992) 665 MR1031244