Algebraic & Geometric Topology Volume 11, issue 2 (2011)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Other MSP Journals

Meridional destabilizing number of knots

Toshio Saito

Algebraic & Geometric Topology 11 (2011) 1205–1242

DOI: 10.2140/agt.2011.11.1205

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