Geometry & Topology Volume 16, issue 2 (2012)

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Knot commensurability and the Berge conjecture

Michel Boileau, Steven Boyer, Radu Cebanu and Genevieve S Walsh

Geometry & Topology 16 (2012) 625–664

DOI: 10.2140/gt.2012.16.625

Bibliography

1	I R Aitchison, J H Rubinstein, Combinatorial cubings, cusps, and the dodecahedral knots, from: "Topology '90 (Columbus, OH, 1990)" (editors B Apanasov, W D Neumann, A W Reid, L Siebenmann), Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 17 MR1184399
2	I R Aitchison, J H Rubinstein, Geodesic surfaces in knot complements, Experiment. Math. 6 (1997) 137 MR1474574
3	M A Armstrong, The fundamental group of the orbit space of a discontinuous group, Proc. Cambridge Philos. Soc. 64 (1968) 299 MR0221488
4	J Berge, The knots in $D^2\times S^1$ which have nontrivial Dehn surgeries that yield $D^2\times S^1$, Topology Appl. 38 (1991) 1 MR1093862
5	M Boileau, B Leeb, J Porti, Geometrization of $3$–dimensional orbifolds, Ann. of Math. 162 (2005) 195 MR2178962
6	F Bonahon, J P Otal, Scindements de Heegaard des espaces lenticulaires, Ann. Sci. École Norm. Sup. 16 (1983) 451 MR740078
7	D Boyd, The A–polynomials of families of symmetric knots, Lecture notes, PIMS-MSRI conference on Knots and Manifolds (University of British Columbia, Vancouver) (2004)
8	K S Brown, Trees, valuations, and the Bieri–Neumann–Strebel invariant, Invent. Math. 90 (1987) 479 MR914847
9	D Calegari, N M Dunfield, Commensurability of $1$–cusped hyperbolic $3$–manifolds, Trans. Amer. Math. Soc. 354 (2002) 2955 MR1895211
10	M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. 125 (1987) 237 MR881270
11	D Gabai, Foliations and the topology of $3$–manifolds, J. Differential Geom. 18 (1983) 445 MR723813
12	D Gabai, Foliations and the topology of $3$–manifolds. II, J. Differential Geom. 26 (1987) 461 MR910017
13	D Gabai, Surgery on knots in solid tori, Topology 28 (1989) 1 MR991095
14	D Gabai, $1$–bridge braids in solid tori, Topology Appl. 37 (1990) 221 MR1082933
15	R E Gompf, $\mathrm{Spin}^c$–structures and homotopy equivalences, Geom. Topol. 1 (1997) 41 MR1475553
16	F González-Acuña, W C Whitten, Imbeddings of three-manifold groups, Mem. Amer. Math. Soc. 99, no. 474, Amer. Math. Soc. (1992) MR1117167
17	O Goodman, D Heard, C Hodgson, Commensurators of cusped hyperbolic manifolds, Experiment. Math. 17 (2008) 283 MR2455701
18	C M Gordon, Dehn surgery and satellite knots, Trans. Amer. Math. Soc. 275 (1983) 687 MR682725
19	C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
20	A Hatcher, Notes on basic $3$–manifold Topology, online book (2007)
21	N Hoffman, Commensurability classes containing three knot complements, Algebr. Geom. Topol. 10 (2010) 663 MR2606796
22	A Juhász, Holomorphic discs and sutured manifolds, Algebr. Geom. Topol. 6 (2006) 1429 MR2253454
23	A Juhász, Floer homology and surface decompositions, Geom. Topol. 12 (2008) 299 MR2390347
24	S Kojima, Isometry transformations of hyperbolic $3$–manifolds, Topology Appl. 29 (1988) 297 MR953960
25	P B Kronheimer, T S Mrowka, Dehn surgery, the fundamental group and SU$(2)$, Math. Res. Lett. 11 (2004) 741 MR2106239
26	M L Macasieb, T W Mattman, Commensurability classes of $(-2,3,n)$ pretzel knot complements, Algebr. Geom. Topol. 8 (2008) 1833 MR2448875
27	J Morgan, G Tian, Ricci flow and the Poincaré conjecture, Clay Math. Monogr. 3, Amer. Math. Soc. (2007) MR2334563
28	W D Neumann, Kleinian groups generated by rotations, from: "Groups—Korea '94 (Pusan)" (editors A C Kim, D L Johnson), de Gruyter (1995) 251 MR1476967
29	W D Neumann, A W Reid, Arithmetic of hyperbolic manifolds, from: "Topology '90 (Columbus, OH, 1990)" (editors B Apanasov, W D Neumann, A W Reid, L Siebenmann), Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter (1992) 273 MR1184416
30	Y Ni, Knot Floer homology detects fibred knots, Invent. Math. 170 (2007) 577 MR2357503
31	Y Ni, Link Floer homology detects the Thurston norm, Geom. Topol. 13 (2009) 2991 MR2546619
32	P Ozsváth, Z Szabó, Knot Floer homology and rational surgeries arXiv:math.GT/0504404
33	P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
34	P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. 159 (2004) 1159 MR2113020
35	P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 MR2113019
36	P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
37	P Ozsváth, Z Szabó, Holomorphic disks, link invariants and the multi-variable Alexander polynomial, Algebr. Geom. Topol. 8 (2008) 615 MR2443092
38	J Rasmussen, Lens space surgeries and L-space homology spheres arXiv:0710.2531v1
39	A W Reid, Arithmeticity of knot complements, J. London Math. Soc. 43 (1991) 171 MR1099096
40	A W Reid, G S Walsh, Commensurability classes of 2-bridge knot complements, Algebr. Geom. Topol. 8 (2008) 1031 MR2443107
41	T Sakai, Geodesic knots in a hyperbolic $3$–manifold, Kobe J. Math. 8 (1991) 81 MR1134707
42	R E Schwartz, The quasi-isometry classification of rank one lattices, Inst. Hautes Études Sci. Publ. Math. (1995) 133 MR1383215
43	J Stallings, On fibering certain $3$–manifolds, from: "Topology of $3$–manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961)" (editor M K Fort), Prentice-Hall (1962) 95 MR0158375
44	J Stallings, Constructions of fibred knots and links, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, CA, 1976), Part 2" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 55 MR520522
45	W P Thurston, A norm for the homology of $3$–manifolds, Mem. Amer. Math. Soc. 59, no. 339, Amer. Math. Soc. (1986) MR823443
46	V Turaev, Torsion invariants of $\mathrm{Spin}^c$–structures on $3$–manifolds, Math. Res. Lett. 4 (1997) 679 MR1484699
47	C A Weibel, An introduction to homological algebra, Cambridge Studies in Adv. Math. 38, Cambridge Univ. Press (1994) MR1269324