On unknotting tunnel systems of satellite chain links
Darlan Gir\~ao, Jo\~ao M. Nogueira, Ant\'onio Salgueiro
TL;DR
This paper establishes a minimal tunnel number for satellite chain links with multiple components, relating it to the bridge number of the companion knot, and demonstrates the sharpness of this bound in specific cases.
Contribution
It provides a new lower bound for the tunnel number of satellite chain links based on the bridge number of the companion knot, with sharpness proven for certain cases.
Findings
The tunnel number of satellite chain links is bounded below by twice the bridge number of the companion.
The bound is sharp for satellite chain links over a 2-bridge knot.
The result characterizes minimal tunnel systems in these links.
Abstract
We prove that the tunnel number of a satellite chain link with a number of components higher than or equal to twice the bridge number of the companion is as small as possible among links with the same number of components. We prove this result to be sharp for satellite chain links over a 2-bridge knot.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Digital Image Processing Techniques