Volume 6, issue 5 (2006)

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Knots with unknotting number 1 and essential Conway spheres

Cameron McA Gordon and John Luecke

Algebraic & Geometric Topology 6 (2006) 2051–2116
Bibliography
1 S A Bleiler, A note on unknotting number, Math. Proc. Cambridge Philos. Soc. 96 (1984) 469 MR757839
2 M Boileau, B Zimmermann, The $\pi$-orbifold group of a link, Math. Z. 200 (1989) 187 MR978294
3 F Bonahon, L C Siebenmann, The characteristic toric splitting of irreducible compact $3$-orbifolds, Math. Ann. 278 (1987) 441 MR909236
4 J H Conway, An enumeration of knots and links, and some of their algebraic properties, from: "Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967)", Pergamon (1970) 329 MR0258014
5 M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. $(2)$ 125 (1987) 237 MR881270
6 M Eudave-Muñoz, Non-hyperbolic manifolds obtained by Dehn surgery on hyperbolic knots, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470720
7 M Eudave-Muñoz, On hyperbolic knots with Seifert fibered Dehn surgeries, from: "Proceedings of the First Joint Japan-Mexico Meeting in Topology (Morelia, 1999)" (2002) 119 MR1903687
8 C M Gordon, Dehn surgery and satellite knots, Trans. Amer. Math. Soc. 275 (1983) 687 MR682725
9 C M Gordon, J Luecke, Only integral Dehn surgeries can yield reducible manifolds, Math. Proc. Cambridge Philos. Soc. 102 (1987) 97 MR886439
10 C M Gordon, J Luecke, Reducible manifolds and Dehn surgery, Topology 35 (1996) 385 MR1380506
11 C M Gordon, J Luecke, Non-integral toroidal Dehn surgeries, Comm. Anal. Geom. 12 (2004) 417 MR2074884
12 W Haken, Theorie der Normalflächen, Acta Math. 105 (1961) 245 MR0141106
13 R Hartley, Knots and involutions, Math. Z. 171 (1980) 175 MR570907
14 W H Jaco, P B Shalen, Seifert fibered spaces in $3$-manifolds, Mem. Amer. Math. Soc. 21 (1979) MR539411
15 T Kanenobu, H Murakami, Two-bridge knots with unknotting number one, Proc. Amer. Math. Soc. 98 (1986) 499 MR857949
16 R Kirby, Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35 MR1470751
17 T Kobayashi, Minimal genus Seifert surfaces for unknotting number $1$ knots, Kobe J. Math. 6 (1989) 53 MR1023526
18 P Kohn, Two-bridge links with unlinking number one, Proc. Amer. Math. Soc. 113 (1991) 1135 MR1079893
19 W B R Lickorish, The unknotting number of a classical knot, from: "Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982)", Contemp. Math. 44, Amer. Math. Soc. (1985) 117 MR813107
20 W H Meeks III, P Scott, Finite group actions on $3$-manifolds, Invent. Math. 86 (1986) 287 MR856847
21 W Menasco, Closed incompressible surfaces in alternating knot and link complements, Topology 23 (1984) 37 MR721450
22 W Menasco, M Thistlethwaite, The classification of alternating links, Ann. of Math. $(2)$ 138 (1993) 113 MR1230928
23 W Menasco, X Zhang, Notes on tangles, 2-handle additions and exceptional Dehn fillings, Pacific J. Math. 198 (2001) 149 MR1831976
24 J M Montesinos, Surgery on links and double branched covers of $S^{3}$, from: "Knots, groups, and $3$-manifolds (Papers dedicated to the memory of R H Fox)" (editor L Neuwirth), Ann. of Math. Studies 84, Princeton Univ. Press (1975) 227 MR0380802
25 K Motegi, A note on unlinking numbers of Montesinos links, Rev. Mat. Univ. Complut. Madrid 9 (1996) 151 MR1413272
26 Y Nakanishi, Unknotting numbers and knot diagrams with the minimum crossings, Math. Sem. Notes Kobe Univ. 11 (1983) 257 MR749196
27 P Ozsváth, Z Szabó, Knots with unknotting number one and Heegaard Floer homology, Topology 44 (2005) 705 MR2136532
28 M G Scharlemann, Unknotting number one knots are prime, Invent. Math. 82 (1985) 37 MR808108
29 M Scharlemann, Producing reducible $3$-manifolds by surgery on a knot, Topology 29 (1990) 481 MR1071370
30 M Scharlemann, A Thompson, Unknotting number, genus, and companion tori, Math. Ann. 280 (1988) 191 MR929535
31 M Scharlemann, A Thompson, Link genus and the Conway moves, Comment. Math. Helv. 64 (1989) 527 MR1022995
32 C Sundberg, M Thistlethwaite, The rate of growth of the number of prime alternating links and tangles, Pacific J. Math. 182 (1998) 329 MR1609591
33 M B Thistlethwaite, On the algebraic part of an alternating link, Pacific J. Math. 151 (1991) 317 MR1132393
34 M Thistlethwaite, On the structure and scarcity of alternating links and tangles, J. Knot Theory Ramifications 7 (1998) 981 MR1654669
35 J L Tollefson, Involutions of Seifert fiber spaces, Pacific J. Math. 74 (1978) 519 MR0645400
36 F Waldhausen, Über Involutionen der $3$-Sphäre, Topology 8 (1969) 81 MR0236916
37 Y Q Wu, Sutured manifold hierarchies, essential laminations, and Dehn surgery, J. Differential Geom. 48 (1998) 407 MR1638025
38 X Zhang, Unknotting number one knots are prime: a new proof, Proc. Amer. Math. Soc. 113 (1991) 611 MR1076582