Twisted torus knots T(p,q,3,s) are tunnel number one
Jung Hoon Lee
TL;DR
This paper proves that a specific class of twisted torus knots, denoted T(p,q,3,s), have tunnel number one, with a simple arc serving as an unknotting tunnel, simplifying their topological understanding.
Contribution
It establishes that twisted torus knots T(p,q,3,s) are tunnel number one and identifies a straightforward unknotting tunnel.
Findings
Twisted torus knots T(p,q,3,s) are tunnel number one.
A short spanning arc between twisted strands acts as an unknotting tunnel.
Simplifies the topological analysis of these knots.
Abstract
We show that twisted torus knots are tunnel number one. A short spanning arc connecting two adjacent twisted strands is an unknotting tunnel.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory