Tunnel leveling, depth, and bridge numbers

DOI10.1090/S0002-9947-2010-05248-1zbMath1210.57004arXiv0812.1396MaRDI QIDQ3082355

Darryl McCullough, Sangbum Cho

Publication date: 10 March 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.1396

zbMATH Keywords

bridge numberdisk complexcabling operationstunnel depthTunnel number 1 knots

Mathematics Subject Classification ID

Related Items (8)

Iterated splitting and the classification of knot tunnels ⋮ Tunnel complexes of 3-manifolds ⋮ Middle tunnels by splitting ⋮ An algorithm for finding parameters of tunnels ⋮ The tunnel number and the cutting number with constituent handlebody-knots ⋮ The tree of knot tunnels ⋮ Cabling sequences of tunnels of torus knots ⋮ Constructing knot tunnels using giant steps

Cites Work

• On unknotting tunnels for knots
• A presentation for the automorphisms of the 3-sphere that preserve a genus two Heegaard splitting
• The tree of knot tunnels
• Cabling sequences of tunnels of torus knots
• Heegaard splittings of Seifert fibered spaces
• Unknotting tunnels in two-bridge knot and link complements
• Levelling an unknotting tunnel
• On Heegaard decompositions of torus knot exteriors and related Seifert fibre spaces
• High distance knots
• Automorphisms of the 3-sphere preserving a genus two Heegaard splitting
• Alternate Heegaard genus bounds distance
• Constructing knot tunnels using giant steps
• ON TANGLE DECOMPOSITIONS OF TUNNEL NUMBER ONE LINKS
• Unknotting Tunnels and Seifert Surfaces
• TUNNELS OF 2-BRIDGE LINKS
• Homeomorphisms of the 3-sphere that preserve a Heegaard splitting of genus two

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