Volume 13, issue 2 (2009)

 1 C C Adams, A W Reid, Unknotting tunnels in two-bridge knot and link complements, Comment. Math. Helv. 71 (1996) 617 MR1420513 2 E Akbas, A presentation for the automorphisms of the 3-sphere that preserve a genus two Heegaard splitting, Pacific J. Math. 236 (2008) 201 MR2407105 3 S Cho, Homeomorphisms of the $3$–sphere that preserve a Heegaard splitting of genus two, Proc. Amer. Math. Soc. 136 (2008) 1113 MR2361888 4 S Cho, D McCullough, Cabling sequences of tunnels of torus knots, Algebr. Geom. Topol. 9 (2009) 1 5 S Cho, D McCullough, Constructing knot tunnels using giant steps arXiv:0812.1382 6 S Cho, D McCullough, Tunnel leveling, depth, and bridge numbers arXiv:0812.1396 7 S Cho, D McCullough, Semisimple tunnels, in preparation 8 S Cho, D McCullough, Software 9 D Futer, Involutions of knots that fix unknotting tunnels, J. Knot Theory Ramifications 16 (2007) 741 MR2341313 10 H Goda, C Hayashi, Genus two Heegaard splittings of exteriors of $1$–genus $1$–bridge knots, preprint 11 H Goda, M Scharlemann, A Thompson, Levelling an unknotting tunnel, Geom. Topol. 4 (2000) 243 MR1778174 12 L Goeritz, Die Abbildungen der Brezelfläche und der Volbrezel vom Gesschlect $2$, Abh. Math. Sem. Univ. Hamburg 9 (1933) 244 13 C M Gordon, On primitive sets of loops in the boundary of a handlebody, Topology Appl. 27 (1987) 285 MR918538 14 T Harikae, On the triviality of bouquets and tunnel number one links, from: "Proceedings of the Workshop on Graph Theory and Related Topics (Sendai, 1999)" (2001) 1 MR1874572 15 J Johnson, Bridge number and the curve complex arXiv:math.GT/0603102 16 J Johnson, A Thompson, On tunnel number one knots which are not $(1,n)$ arXiv:J. Knot Theory Ramifications 17 T Kobayashi, A criterion for detecting inequivalent tunnels for a knot, Math. Proc. Cambridge Philos. Soc. 107 (1990) 483 MR1041480 18 T Kobayashi, Classification of unknotting tunnels for two bridge knots, from: "Proceedings of the Kirbyfest (Berkeley, CA, 1998)" (editors J Hass, M Scharlemann), Geom. Topol. Monogr. 2 (1999) 259 MR1734412 19 M Kuhn, Tunnels of $2$–bridge links, J. Knot Theory Ramifications 5 (1996) 167 MR1395777 20 D McCullough, Virtually geometrically finite mapping class groups of $3$–manifolds, J. Differential Geom. 33 (1991) 1 MR1085134 21 Y N Minsky, Y Moriah, S Schleimer, High distance knots, Algebr. Geom. Topol. 7 (2007) 1471 MR2366166 22 K Morimoto, M Sakuma, On unknotting tunnels for knots, Math. Ann. 289 (1991) 143 MR1087243 23 T Saito, Scharlemann–Thompson invariant for knots with unknotting tunnels and the distance of $(1,1)$–splittings, J. London Math. Soc. $(2)$ 71 (2005) 801 MR2132384 24 M Scharlemann, Automorphisms of the $3$–sphere that preserve a genus two Heegaard splitting, Bol. Soc. Mat. Mexicana $(3)$ 10 (2004) 503 MR2199366 25 M Scharlemann, There are no unexpected tunnel number one knots of genus one, Trans. Amer. Math. Soc. 356 (2004) 1385 MR2034312 26 M Scharlemann, A Thompson, Unknotting tunnels and Seifert surfaces, Proc. London Math. Soc. $(3)$ 87 (2003) 523 MR1990938 27 Y Uchida, Detecting inequivalence of some unknotting tunnels for two-bridge knots, from: "Algebra and topology 1990 (Taejon, 1990)" (editors S H Bae, G T Jin), Korea Adv. Inst. Sci. Tech. (1990) 227 MR1098731