Geometry & Topology Monographs 12
(2007) 401–411
|
1 |
E Akbas, A
presentation for the automorphisms of the 3-sphere that
preserve a genus two Heegaard splitting arXiv:math.GT/0504519 |
2 |
D Bachman, Heegaard
splittings with boundary and almost normal surfaces,
Topology Appl. 116 (2001) 153–184 MR1855961 |
3 |
D Bachman, R
Derby-Talbot, Non-isotopic
Heegaard splittings of Seifert fibered spaces, Algebr.
Geom. Topol. 6 (2006) 351–372 MR2220681
With an appendix by R Weidmann |
4 |
D Bachman, S
Schleimer, E Sedgwick, Sweepouts of
amalgamated 3-manifolds, Algebr. Geom. Topol. 6 (2006)
171–194 MR2199458 |
5 |
M Eudave-Muñoz,
Incompressible
surfaces in tunnel number one knot complements,
Topology Appl. 98 (1999) 167–189 MR1719999
II Iberoamerican Conference on Topology and its Applications
(Morelia, 1997) |
6 |
M Eudave-Muñoz,
Essential meridional surfaces for tunnel number one
knots, Bol. Soc. Mat. Mexicana (3) 6 (2000) 263–277
MR1810854 |
7 |
M Eudave-Muñoz,
Incompressible
surfaces and (1,1)–knots, J. Knot Theory
Ramifications 15 (2006) 935–948 MR2251034 |
8 |
M Eudave-Muñoz,
Incompressible
surfaces and (1,2)–knots, Geom. Topol. Monogr. 12
(2007) 35–87 |
9 |
M Eudave-Muñoz,
E Ramírez-Losada, Meridional surfaces and
(1,1)–knots, Trans. Amer. Math. Soc. to appear
arXiv:math.GT/0608205 |
10 |
D Gabai, G R
Meyerhoff, N Thurston, Homotopy
hyperbolic 3-manifolds are hyperbolic, Ann. of Math.
(2) 157 (2003) 335–431 MR1973051 |
11 |
L Goeritz, Die
Abbildungen der Brezelfläche und der Vollbrezel vom
Geschlect 2, Abh. Math. Sem. Univ. Hamburg 9 (1933)
244–259 |
12 |
J Hempel, 3-manifolds
as viewed from the curve complex, Topology 40 (2001)
631–657 MR1838999 |
13 |
W Jaco, E
Sedgwick, Decision
problems in the space of Dehn fillings, Topology 42
(2003) 845–906 MR1958532 |
14 |
J Johnson, A
Thompson, On tunnel number one knots which are not
(1,n) arXiv:math.GT/0606226 |
15 |
T Kobayashi,
Structures of the Haken manifolds with Heegaard splittings
of genus two, Osaka J. Math. 21 (1984) 437–455
MR752472 |
16 |
T Kobayashi, Y
Rieck, On the growth rate
of the tunnel number of knots, J. Reine Angew. Math.
592 (2006) 63–78 MR2222730 |
17 |
T Kobayashi, Y
Rieck, Knot exteriors with additive Heegaard genus and
Morimoto's Conjecture arXiv:math.GT/0701765 |
18 |
T Kobayashi, Y
Rieck, Heegaard genus of the connected sum of m-small
knots, preprint |
19 |
T Li, Heegaard surfaces
and measured laminations. I. The Waldhausen conjecture,
Invent. Math. 167 (2007) 135–177 MR2264807 |
20 |
T Li, On the
Heegaard splittings of amalgamated 3–manifolds,
preprint |
21 |
M Lustig, Y
Moriah, A finiteness
result for Heegaard splittings, Topology 43 (2004)
1165–1182 MR2079999 |
22 |
Y Minsky, Y
Moriah, S Schleimer, High distance knots
arXiv:math.gt/0607265 |
23 |
Y Moriah, Heegaard splittings
of knot exteriors, Geom. Topol. Monogr. 12 (2007)
191–232 |
24 |
Y Moriah, H
Rubinstein, Heegaard structures of negatively curved
3-manifolds, Comm. Anal. Geom. 5 (1997) 375–412
MR1487722 |
25 |
Y Moriah, S
Schleimer, E Sedgwick, Heegaard
splittings of the form H+nK, Comm. Anal. Geom. 14
(2006) 215–247 MR2255010 |
26 |
Y Moriah, E
Sedgwick, Twist knots and weakly reducible Heegaard
splittings, preprint |
27 |
K Morimoto,
There are knots
whose tunnel numbers go down under connected sum, Proc.
Amer. Math. Soc. 123 (1995) 3527–3532 MR1317043 |
28 |
K Morimoto, M
Sakuma, On unknotting tunnels
for knots, Math. Ann. 289 (1991) 143–167 MR1087243 |
29 |
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) 113–118 MR1356163 |
30 |
H Namazi, Big
handlebody distance implies finite mapping class group
arXiv:math.gt/0406551 |
31 |
H Namazi, Heegaard
splittings and hyperbolic geometry, PhD thesis, Stony Brook
University (2005) |
32 |
H Namazi, J
Souto, Heegaard splittings and pseudo-Anosov maps,
preprint |
33 |
E Ramírez-Losada,
L G Valdez-Sánchez, Crosscap number two
knots in S3 with (1,1) decompositions, Bol. Soc.
Mat. Mexicana (3) 10 (2004) 451–465 MR2199363 |
34 |
J H Rubinstein,
Problems
on 3–manifolds, Geom. Topol. Monogr. 12 (2007)
285–298 |
35 |
M Sakuma, Manifolds
with infinitely many non-isotopic Heegaard splittings of
minimal genus, preprint |
36 |
M Scharlemann,
Automorphisms of the 3-sphere that preserve a genus two
Heegaard splitting, Bol. Soc. Mat. Mexicana (3) 10 (2004)
503–514 MR2199366 |
37 |
M Scharlemann, M
Tomova, Alternate Heegaard
genus bounds distance, Geom. Topol. 10 (2006)
593–617 MR2224466 |
38 |
K Shackleton,
Tightness and computing distances in the curve complex
arXiv:math.GT/0412078 |
39 |
J Souto, The
Heegaard genus and distances in the curve complex,
preprint |
40 |
M Tomova, Distance
of Heegaard splittings of knot complements arXiv:math.GT/0703474 |