1
|
M Culler, C M
Gordon, J Luecke, P B Shalen,
Dehn
surgery on knots, Ann. of Math. (2) 125 (1987)
237–300 MR881270
|
2
|
D Gabai, Foliations and
the topology of 3–manifolds III, J.
Differential Geom. 26 (1987) 479–536 MR910018
|
3
|
H Goda, M
Scharlemann, A Thompson, Levelling
an unknotting tunnel, Geom. Topol. 4 (2000)
243–275 MR1778174
|
4
|
C Hayashi, K
Shimokawa, Thin position of a pair
(3–manifold, 1–submanifold), Pacific J.
Math. 197 (2001) 301–324 MR1815259
|
5
|
D J Heath, T
Kobayashi, Essential tangle decomposition from
thin position of a link, Pacific J. Math. 179
(1997) 101–117 MR1452527
|
6
|
D J Heath, T
Kobayashi, Locally thin position for a link,
Kobe J. Math. 20 (2003) 1–10 MR2102296
|
7
|
D J Heath, T
Kobayashi, A search
method for thin positions of links, Algebr.
Geom. Topol. 5 (2005) 1027–1050 MR2171802
|
8
|
J Hempel,
3–manifolds, AMS Chelsea Publishing,
Providence, RI (2004) MR2098385
(reprint of the 1976 original)
|
9
|
H Howards, J
Schultens, Thin position for knots and
3–manifolds, preprint
|
10
|
W Jaco, Lectures on
three-manifold topology, CBMS Regional Conference
Series in Mathematics 43, American Mathematical
Society, Providence, R.I. (1980) MR565450
|
11
|
T Kobayashi, Y Rieck,
Knot exteriors with additive Heegaard genus and
Morimoto's conjecture arXiv:math/0701765
|
12
|
T Kobayashi, Y Rieck,
Knots with g(e(k)) = 2 and g(e(k#k#k)) = 6 and
Morimoto's conjecture arXiv:math/0701766
|
13
|
T Kobayashi, Y Rieck,
Heegaard genus of the connected sum of m–small
knots, Comm. Anal. Geom. 14 (2006)
1037–1077 MR2287154
|
14
|
K Morimoto, On the super
additivity of tunnel number of knots, Math.
Ann. 317 (2000) 489–508 MR1776114
|
15
|
K Morimoto, J
Schultens, Tunnel
numbers of small knots do not go down under connected
sum, Proc. Amer. Math. Soc. 128 (2000)
269–278 MR1641065
|
16
|
Y Rieck, Heegaard
structures of manifolds in the Dehn filling
space, Topology 39 (2000) 619–641
MR1746912
|
17
|
Y Rieck, J H
Rubinstein, Invariant Heegaard surfaces in
manifolds with involutions and the Heegaard genus of
double covers arXiv:math/0607145
|
18
|
Y Rieck, E Sedgwick,
Finiteness results for Heegaard surfaces in surgered
manifolds, Comm. Anal. Geom. 9 (2001) 351–367
MR1846207
|
19
|
Y Rieck, E Sedgwick,
Thin
position for a connected sum of small knots,
Algebr. Geom. Topol. 2 (2002) 297–309 MR1917054
|
20
|
J H Rubinstein,
Polyhedral minimal surfaces, Heegaard splittings and
decision problems for 3–dimensional
manifolds, from: "Geometric topology (Athens, GA,
1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc.,
Providence, RI (1997) 1–20 MR1470718
|
21
|
T Saito, M
Scharlemann, J Schultens, Lecture notes
on generalized Heegaard splittings arXiv:math/0504167
|
22
|
M Scharlemann, Thin
position in the theory of classical knots, from:
"Handbook of knot theory", Elsevier B. V., Amsterdam
(2005) 429–459 MR2179267
|
23
|
M Scharlemann, J
Schultens, Annuli in
generalized Heegaard splittings and degeneration of
tunnel number, Math. Ann. 317 (2000)
783–820 MR1777119
|
24
|
M Scharlemann, J
Schultens, 3–manifolds
with planar presentations and the width of satellite
knots, Trans. Amer. Math. Soc. 358 (2006)
3781–3805 MR2218999
|
25
|
M Scharlemann, A
Thompson, Thin position and Heegaard splittings
of the 3–sphere, J. Differential Geom. 39
(1994) 343–357 MR1267894
|
26
|
M Scharlemann, A
Thompson, Thin position for
3–manifolds, from: "Geometric topology
(Haifa, 1992)", Contemp. Math. 164, Amer. Math. Soc.,
Providence, RI (1994) 231–238 MR1282766
|
27
|
M Scharlemann, A
Thompson, On the
additivity of knot width, from: "Proceedings of
the Casson Fest", Geom. Topol. Monogr. 7, Geom. Topol.
Publ., Coventry (2004) 135–144 MR2172481
|
28
|
H Schubert, Über
eine numerische Knoteninvariante, Math. Z. 61
(1954) 245–288
|
29
|
J Schultens, Bridge
numbers of torus knots, to appear in Math. Proc.
Cambridge Philos. Soc.
|
30
|
J Schultens, The
classification of Heegaard splittings for (compact
orientable surface) × S¹,
Proc. London Math. Soc. (3) 67 (1993) 425–448
MR1226608
|
31
|
J Schultens, Additivity
of bridge numbers of knots, Math. Proc.
Cambridge Philos. Soc. 135 (2003) 539–544
MR2018265
|
32
|
A Thompson, Thin
position and bridge number for knots in the
3–sphere, Topology 36 (1997)
505–507 MR1415602
|
33
|
M Tomova, Compressing
thin spheres in the complement of a link,
Topology Appl. 153 (2006) 2987–2999 MR2248402
|
34
|
Y-Q Wu, Thin
position and essential planar surfaces, Proc.
Amer. Math. Soc. 132 (2004) 3417–3421 MR2073319
|