#### Volume 22, issue 1 (2022)

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On unknotting tunnel systems of satellite chain links

### Darlan Girão, João Miguel Nogueira and António Salgueiro

Algebraic & Geometric Topology 22 (2022) 307–323
##### 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.

 Dedicated to the memory of Darlan Girão
##### Keywords
chain link, tunnel number, bridge number, rank versus genus conjecture
Primary: 57K10
Secondary: 57K32
##### Publication
Revised: 27 November 2020
Accepted: 21 February 2021
Published: 26 April 2022
##### Authors
 Darlan Girão Department of Mathematics Universidade Federal do Ceará Fortaleza, CE Brazil João Miguel Nogueira CMUC, Department of Mathematics University of Coimbra Coimbra Portugal António Salgueiro CMUC, Department of Mathematics University of Coimbra Coimbra Portugal