Algebraic & Geometric Topology Volume 11, issue 1 (2011)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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Tunnel complexes of $3$–manifolds

Yuya Koda

Algebraic & Geometric Topology 11 (2011) 417–447

DOI: 10.2140/agt.2011.11.417

Bibliography

1	M Boileau, M Rost, H Zieschang, On Heegaard decompositions of torus knot exteriors and related Seifert fibre spaces, Math. Ann. 279 (1988) 553 MR922434
2	F Bonahon, J P Otal, Scindements de Heegaard des espaces lenticulaires, Ann. Sci. École Norm. Sup. $(4)$ 16 (1983) MR740078
3	S Cho, D McCullough, Cabling sequences of tunnels of torus knots, Algebr. Geom. Topol. 9 (2009) 1 MR2471129
4	S Cho, D McCullough, The tree of knot tunnels, Geom. Topol. 13 (2009) 769 MR2469530
5	S Cho, D McCullough, Constructing knot tunnels using giant steps, Proc. Amer. Math. Soc. 138 (2010) 375 MR2550203
6	S Cho, D McCullough, Tunnel leveling, depth, and bridge numbers, Trans. Amer. Math. Soc. 363 (2011) 259 MR2719681
7	H Goda, C Hayashi, Genus two Heegaard splittings of exteriors of $1$–genus $1$–bridge knots arXiv:1009.2134
8	H Goda, M Scharlemann, A Thompson, Levelling an unknotting tunnel, Geom. Topol. 4 (2000) 243 MR1778174
9	C M Gordon, On primitive sets of loops in the boundary of a handlebody, Topology Appl. 27 (1987) 285 MR918538
10	J Hass, A Thompson, W Thurston, Stabilization of Heegaard splittings, Geom. Topol. 13 (2009) 2029 MR2507114
11	J Hempel, $3$-Manifolds as viewed from the curve complex, Topology 40 (2001) 631 MR1838999
12	M Hirasawa, Y Uchida, The Gordian complex of knots, from: "Knots 2000 Korea, Vol. 1 (Yongpyong)", J. Knot Theory Ramifications 11 (2002) 363 MR1905691
13	A Ishii, Moves and invariants for knotted handlebodies, Algebr. Geom. Topol. 8 (2008) 1403 MR2443248
14	A Ishii, K Kishimoto, The IH–complex of spatial trivalent graphs (2009)
15	J Johnson, Bridge number and the curve complex arXiv:math.GT/0603102
16	J Johnson, A Thompson, On tunnel number one knots that are not $(1,n)$ arXiv:math/0606226v3
17	A Kawauchi, A survey of knot theory, Birkhäuser Verlag (1996) MR1417494
18	S Kinoshita, On $\theta_n$–curves in $\mathbf{R}^3$ and their constituent knots, from: "Topology and computer science (Atami, 1986)" (editor S Suzuki), Kinokuniya (1987) 211 MR1112593
19	T Kobayashi, Classification of unknotting tunnels for two bridge knots, from: "Proceedings of the Kirbyfest (Berkeley, CA, 1998)" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2 (1999) 259 MR1734412
20	F Luo, On Heegaard diagrams, Math. Res. Lett. 4 (1997) 365 MR1453066
21	D McCullough, Virtually geometrically finite mapping class groups of $3$–manifolds, J. Differential Geom. 33 (1991) 1 MR1085134
22	Y Moriah, Heegaard splittings of Seifert fibered spaces, Invent. Math. 91 (1988) 465 MR928492
23	K Morimoto, M Sakuma, On unknotting tunnels for knots, Math. Ann. 289 (1991) 143 MR1087243
24	K Morimoto, M Sakuma, Y Yokota, Examples of tunnel number one knots which have the property “$1+1=3$”, Math. Proc. Cambridge Philos. Soc. 119 (1996) 113 MR1356163
25	M Scharlemann, M Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006) 593 MR2224466
26	F Waldhausen, Heegaard-Zerlegungen der $3$–Sphäre, Topology 7 (1968) 195 MR0227992