Volume 11, issue 2 (2011)

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

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Meridional destabilizing number of knots

Toshio Saito

Algebraic & Geometric Topology 11 (2011) 1205–1242
Bibliography
1 A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275 MR918537
2 H Doll, A generalized bridge number for links in 3–manifolds, Math. Ann. 294 (1992) 701 MR1190452
3 C M Gordon, A W Reid, Tangle decompositions of tunnel number one knots and links, J. Knot Theory Ramifications 4 (1995) 389 MR1347361
4 C Hayashi, K Shimokawa, Thin position of a pair (3–manifold, 1–submanifold), Pacific J. Math. 197 (2001) 301 MR1815259
5 J Johnson, A Thompson, On tunnel number one knots which are not (1,n) arXiv:math.GT/0606226
6 T Kobayashi, Y Rieck, Heegaard genus of the connected sum of m–small knots, Comm. Anal. Geom. 14 (2006) 1037 MR2287154
7 T Kobayashi, Y Rieck, Knot exteriors with additive Heegaard genus and Morimoto’s conjecture, Algebr. Geom. Topol. 8 (2008) 953 MR2443104
8 T Kobayashi, Y Rieck, Knots with g(E(K)) = 2 and g(E(K#K#K)) = 6 and Morimoto’s conjecture, Topology Appl. 156 (2009) 1114 MR2493371
9 T Kobayashi, T Saito, Destabilizing Heegaard splittings of knot exteriors, Topology Appl. 157 (2010) 202 MR2556098
10 Y N Minsky, Y Moriah, S Schleimer, High distance knots, Algebr. Geom. Topol. 7 (2007) 1471 MR2366166
11 K Morimoto, On the additivity of tunnel number of knots, Topology Appl. 53 (1993) 37 MR1243869
12 K Morimoto, Tunnel number, connected sum and meridional essential surfaces, Topology 39 (2000) 469 MR1746903
13 K Morimoto, Characterization of composite knots with 1–bridge genus two, J. Knot Theory Ramifications 10 (2001) 823 MR1840270
14 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
15 M Scharlemann, J Schultens, The tunnel number of the sum of n knots is at least n, Topology 38 (1999) 265 MR1660345
16 H Schubert, Über eine numerische Knoteninvariante, Math. Z. 61 (1954) 245 MR0072483
17 J Schultens, Additivity of tunnel number for small knots, Comment. Math. Helv. 75 (2000) 353 MR1793793
18 M Tomova, Thin position for knots in a 3–manifold, J. Lond. Math. Soc. (2) 80 (2009) 85 MR2520379