Geometry & Topology Volume 17, issue 1 (2013)

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Width is not additive

Ryan Blair and Maggy Tomova

Geometry & Topology 17 (2013) 93–156

DOI: 10.2140/gt.2013.17.93

Bibliography

1	R C Blair, Bridge number and Conway products, Algebr. Geom. Topol. 10 (2010) 789 MR2629764
2	R Blair, M Tomova, Companions of the unknot and width additivity, J. Knot Theory Ramifications 20 (2011) 497 MR2796224
3	R Blair, M Tomova, M Yoshizawa, High distance bridge surfaces arXiv:1203.4294
4	J H Conway, An enumeration of knots and links, and some of their algebraic properties, from: "Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967)" (editor J Leech), Pergamon (1970) 329 MR0258014
5	D Gabai, Foliations and the topology of 3–manifolds. III, J. Differential Geom. 26 (1987) 479 MR910018
6	H Goda, M Scharlemann, A Thompson, Levelling an unknotting tunnel, Geom. Topol. 4 (2000) 243 MR1778174
7	C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
8	D J Heath, T Kobayashi, A search method for thin positions of links, Algebr. Geom. Topol. 5 (2005) 1027 MR2171802
9	J Johnson, M Tomova, Flipping bridge surfaces and bounds on the stable bridge number arXiv:0908.3690
10	L H Kauffman, S Lambropoulou, Classifying and applying rational knots and rational tangles, from: "Physical knots : knotting, linking, and folding geometric objects in ℝ3 (Las Vegas, NV, 2001)" (editors J A Calvo, K C Millett, E J Rawdon), Contemp. Math. 304, Amer. Math. Soc. (2002) 223 MR1953344
11	Y Rieck, E Sedgwick, Thin position for a connected sum of small knots, Algebr. Geom. Topol. 2 (2002) 297 MR1917054
12	J H Rubinstein, An algorithm to recognize the 3–sphere, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)" (editor S D Chatterji), Birkhäuser (1995) 601 MR1403961
13	M Scharlemann, Thin position in the theory of classical knots, from: "Handbook of knot theory" (editors W Menasco, M Thistlethwaite), Elsevier (2005) 429 MR2179267
14	M Scharlemann, J Schultens, 3–manifolds with planar presentations and the width of satellite knots, Trans. Amer. Math. Soc. 358 (2006) 3781 MR2218999
15	M Scharlemann, A Thompson, On the additivity of knot width, from: "Proceedings of the Casson Fest" (editors C Gordon, Y Rieck), Geom. Topol. Monogr. 7 (2004) 135 MR2172481
16	H Schubert, Über eine numerische Knoteninvariante, Math. Z. 61 (1954) 245 MR0072483
17	H Schubert, Knoten mit zwei Brücken, Math. Z. 65 (1956) 133 MR0082104
18	J Schultens, Additivity of bridge numbers of knots, Math. Proc. Cambridge Philos. Soc. 135 (2003) 539 MR2018265
19	A Thompson, Thin position and the recognition problem for S³, Math. Res. Lett. 1 (1994) 613 MR1295555
20	M Tomova, Compressing thin spheres in the complement of a link, Topology Appl. 153 (2006) 2987 MR2248402
21	M Tomova, Multiple bridge surfaces restrict knot distance, Algebr. Geom. Topol. 7 (2007) 957 MR2336246
22	M Tomova, Cut-disks for level spheres in link and tangle complements, Topology Appl. 156 (2009) 783 MR2492962
23	Y Q Wu, Thin position and essential planar surfaces, Proc. Amer. Math. Soc. 132 (2004) 3417 MR2073319