scholarly journals Levelling an unknotting tunnel

2000 ◽  
Vol 4 (1) ◽  
pp. 243-275 ◽  
Author(s):  
Hiroshi Goda ◽  
Martin Scharlemann ◽  
Abigail Thompson
Keyword(s):  
Unknotting Tunnel

TUNNELS OF 2-BRIDGE LINKS

1996 ◽  
Vol 05 (02) ◽  
pp. 167-171 ◽  
Author(s):  
MARTIN KUHN
Keyword(s):  
Unknotting Tunnel

In the class of links with one unknotting tunnel the 2-bridge links are characterized by the property of consisting of two trivial components. The tunnels of 2-bridge links are classified.

scholarly journals UNKNOTTING TUNNELS, BRACELETS AND THE ELDER SIBLING PROPERTY FOR HYPERBOLIC 3-MANIFOLDS

2013 ◽  
Vol 95 (1) ◽  
pp. 1-19
Author(s):  
COLIN ADAMS ◽  
KARIN KNUDSON
Keyword(s):  
Open Neighborhood ◽  
Sufficient Conditions ◽  
Universal Cover ◽  
Manifold With Boundary ◽  
The One ◽  
Unknotting Tunnel

AbstractAn unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic $\alpha $ in a hyperbolic 3-manifold $M$, we find sufficient conditions for it to be an unknotting tunnel. In particular, if $\alpha $ corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover and has short enough length, it must be an unknotting tunnel. Furthermore, we consider a vertical geodesic $\alpha $ that satisfies the elder sibling property, which means that in the universal cover, every horoball except the one centered at $\infty $ is connected to a larger horoball by a lift of $\alpha $. Such an $\alpha $ with length less than $\ln (2)$ is then shown to be an unknotting tunnel.

scholarly journals TWISTED TORUS KNOTS T(p, q; 3, s) ARE TUNNEL NUMBER ONE

2011 ◽  
Vol 20 (06) ◽  
pp. 807-811 ◽  
Author(s):  
JUNG HOON LEE
Keyword(s):  
Torus Knots ◽  
Tunnel Number ◽  
Unknotting Tunnel

We show that twisted torus knots T(p, q; 3, s) are tunnel number one. A short spanning arc connecting two adjacent twisted strands is an unknotting tunnel.

Examples of tunnel number one knots which have the property ‘1 + 1 = 3’

1996 ◽  
Vol 119 (1) ◽  
pp. 113-118 ◽  
Author(s):  
Kanji Morimoto ◽  
Makoto Sakuma ◽  
Yoshiyuki Yokota
Keyword(s):  
The Family ◽  
Regular Neighbourhood ◽  
Single Arc ◽  
Minimum Number ◽  
Complementary Space ◽  
Tunnel Number ◽  
Tunnel System ◽  
Tunnel Number One Knots ◽  
Unknotting Tunnel

Let K be a knot in the 3-sphere S3, N(K) the regular neighbourhood of K and E(K) = cl(S3−N(K)) the exterior of K. The tunnel number t(K) is the minimum number of mutually disjoint arcs properly embedded in E(K) such that the complementary space of a regular neighbourhood of the arcs is a handlebody. We call the family of arcs satisfying this condition an unknotting tunnel system for K. In particular, we call it an unknotting tunnel if the system consists of a single arc.

scholarly journals INVOLUTIONS OF KNOTS THAT FIX UNKNOTTING TUNNELS

2007 ◽  
Vol 16 (06) ◽  
pp. 741-748 ◽  
Author(s):  
DAVID FUTER
Keyword(s):  
Unknotting Tunnel

Let K be a knot that has an unknotting tunnel τ. We prove that K admits a strong involution that fixes τ pointwise if and only if K is a two-bridge knot and τ its upper or lower tunnel.

Sign in / Sign up

Export Citation Format

Share Document