Volume 12 (2007)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
 
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN 1464-8997 (online)
ISSN 1464-8989 (print)
 
MSP Books and Monographs
Other MSP Publications

Incompressible surfaces and (1,2)–knots

Mario Eudave-Muñoz

Geometry & Topology Monographs 12 (2007) 35–87

DOI: 10.2140/gtm.2007.12.35

Bibliography
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 H Doll, A generalized bridge number for links in 3-manifolds, Math. Ann. 294 (1992) 701–717 MR1190452
3 M Eudave Muñoz, On nonsimple 3-manifolds and 2-handle addition, Topology Appl. 55 (1994) 131–152 MR1256216
4 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)
5 M Eudave-Muñoz, Essential meridional surfaces for tunnel number one knots, Bol. Soc. Mat. Mexicana (3) 6 (2000) 263–277 MR1810854
6 M Eudave-Muñoz, Incompressible surfaces and (1,1)-knots, J. Knot Theory Ramifications 15 (2006) 935–948 MR2251034
7 M Eudave-Muñoz, M Neumann-Coto, Acylindrical surfaces in 3-manifolds and knot complements, Bol. Soc. Mat. Mexicana (3) 10, Special Issue (2004) 147–169 MR2199345
8 M Eudave Muñoz, E Ramírez-Losada, Meridional surfaces and (1,1)–knots, to appear in Trans. Amer. Math. Soc. arXiv:math.GT/0608205
9 M Eudave Muñoz, E Ramírez-Losada, Meridional tori and (1,2)-knots, in preparation
10 E Finkelstein, Y Moriah, Tubed incompressible surfaces in knot and link complements, Topology Appl. 96 (1999) 153–170 MR1702308
11 C M Gordon, R A Litherland, Incompressible surfaces in branched coverings, from: "The Smith conjecture (New York, 1979)", Pure Appl. Math. 112, Academic Press (1984) 139–152 MR758466
12 C M Gordon, A W Reid, Tangle decompositions of tunnel number one knots and links, J. Knot Theory Ramifications 4 (1995) 389–409 MR1347361
13 A Hatcher, W Thurston, Incompressible surfaces in 2-bridge knot complements, Invent. Math. 79 (1985) 225–246 MR778125
14 J Johnson, A Thompson, On tunnel number one knots which are not (1,n) arXiv:math.GT/0606226
15 Y Minsky, Y Moriah, S Schleimer, High distance knots, Algebr. Geom. Topol. 7 (2007) 1471–1483
16 Y Moriah, H Rubinstein, Heegaard structures of negatively curved 3-manifolds, Comm. Anal. Geom. 5 (1997) 375–412 MR1487722
17 K Morimoto, M Sakuma, On unknotting tunnels for knots, Math. Ann. 289 (1991) 143–167 MR1087243
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) 113–118 MR1356163
19 M Ozawa, Closed incompressible surfaces of genus 2 in 3–bridge knot complements arXiv:math.GT/0702867
20 E Ramírez-Losada, L G Valdez-Sánchez, Personal communication
21 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
22 T Saito, Satellite (1,1)-knots and meridionally incompressible surfaces, Topology Appl. 149 (2005) 33–56 MR2130857
23 H Schubert, Über eine numerische Knoteninvariante, Math. Z. 61 (1954) 245–288 MR0072483
24 Y Q Wu, Incompressibility of surfaces in surgered 3-manifolds, Topology 31 (1992) 271–279 MR1167169
25 Y Q Wu, Incompressible surfaces in link complements, Proc. Amer. Math. Soc. 129 (2001) 3417–3423 MR1845021