Volume 8, issue 2 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Knot exteriors with additive Heegaard genus and Morimoto's Conjecture

Tsuyoshi Kobayashi and Yo’av Rieck

Algebraic & Geometric Topology 8 (2008) 953–969
Bibliography
1 A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275 MR918537
2 K Hartshorn, Heegaard splittings of Haken manifolds have bounded distance, Pacific J. Math. 204 (2002) 61 MR1905192
3 J Hempel, $3$–manifolds as viewed from the curve complex, Topology 40 (2001) 631 MR1838999
4 W Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Math. 43, Amer. Math. Soc. (1980) MR565450
5 J Johnson, Bridge number and the curve complex arXiv:math.GT/0603102
6 J Johnson, A Thompson, On tunnel number one knots which are not $(1,n)$ arXiv:math.GT/0606226v3
7 T Kobayashi, Y Rieck, Knots with $g(E(K)) = 2$ and $g(E(3K)) = 6$ and Morimoto's Conjecture, to appear in Topology Appl. (special volume dedicated to Yves Mathieu and Michel Domergue) arXiv:math.GT/0701766
8 T Kobayashi, Y Rieck, Local detection of strongly irreducible Heegaard splittings via knot exteriors, Topology Appl. 138 (2004) 239 MR2035483
9 T Kobayashi, Y Rieck, Heegaard genus of the connected sum of $m$–small knots, Comm. Anal. Geom. 14 (2006) 1037 MR2287154
10 T Kobayashi, Y Rieck, On the growth rate of the tunnel number of knots, J. Reine Angew. Math. 592 (2006) 63 MR2222730
11 Y N Minsky, Y Moriah, S Schleimer, High distance knots, Algebr. Geom. Topol. 7 (2007) 1471 MR2366166
12 K Miyazaki, Conjugation and the prime decomposition of knots in closed, oriented $3$–manifolds, Trans. Amer. Math. Soc. 313 (1989) 785 MR997679
13 Y Moriah, Heegaard splittings of knot exteriors arXiv:math.GT/0608137
14 Y Moriah, On boundary primitive manifolds and a theorem of Casson–Gordon, Topology Appl. 125 (2002) 571 MR1935173
15 Y Moriah, H Rubinstein, Heegaard structures of negatively curved $3$–manifolds, Comm. Anal. Geom. 5 (1997) 375 MR1487722
16 Y Moriah, E Sedgwick, The Heegaard structure of Dehn filled manifolds arXiv:math.GT/07061927v1
17 K Morimoto, On the super additivity of tunnel number of knots, Math. Ann. 317 (2000) 489 MR1776114
18 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
19 Y Rieck, Heegaard structures of manifolds in the Dehn filling space, Topology 39 (2000) 619 MR1746912
20 Y Rieck, E Sedgwick, Finiteness results for Heegaard surfaces in surgered manifolds, Comm. Anal. Geom. 9 (2001) 351 MR1846207
21 Y Rieck, E Sedgwick, Persistence of Heegaard structures under Dehn filling, Topology Appl. 109 (2001) 41 MR1804562
22 M Scharlemann, Proximity in the curve complex: boundary reduction and bicompressible surfaces, Pacific J. Math. 228 (2006) 325 MR2274524
23 M Scharlemann, J Schultens, Comparing Heegaard and JSJ structures of orientable $3$–manifolds, Trans. Amer. Math. Soc. 353 (2001) 557 MR1804508
24 M Scharlemann, M Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006) 593 MR2224466
25 J Schultens, The classification of Heegaard splittings for (compact orientable surface)$ \times  S^1$, Proc. London Math. Soc. $(3)$ 67 (1993) 425 MR1226608
26 J Schultens, Additivity of tunnel number for small knots, Comment. Math. Helv. 75 (2000) 353 MR1793793
27 E Sedgwick, Genus two $3$–manifolds are built from handle number one pieces, Algebr. Geom. Topol. 1 (2001) 763 MR1875617
28 M Tomova, Distance of Heegaard splittings of knot complements arXiv:math.GT/0703474v2