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

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

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chain link, tunnel number, bridge number, rank versus genus conjecture
Mathematical Subject Classification
Primary: 57K10
Secondary: 57K32
Received: 6 May 2020
Revised: 27 November 2020
Accepted: 21 February 2021
Published: 26 April 2022
Darlan Girão
Department of Mathematics
Universidade Federal do Ceará
Fortaleza, CE
João Miguel Nogueira
CMUC, Department of Mathematics
University of Coimbra
António Salgueiro
CMUC, Department of Mathematics
University of Coimbra