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The bridge number of arborescent links with many twigs

Sebastian Baader, Ryan Blair, Alexandra Kjuchukova and Filip Misev

Algebraic & Geometric Topology 23 (2023) 75–85
Abstract

We prove the meridional rank conjecture for arborescent links associated to plane trees with the following property: all branching points carry a straight branch to at least three leaves. The proof involves obtaining an upper bound on the bridge number in terms of the maximal number of link components of the underlying tree, which is valid for all arborescent links.

Keywords
bridge number, meridional rank, arborescent links, Coxeter quotients
Mathematical Subject Classification
Primary: 57K10
Secondary: 20F55
References
Publication
Received: 26 August 2020
Revised: 28 July 2021
Accepted: 14 October 2021
Published: 27 March 2023
Authors
Sebastian Baader
Mathematisches Institut
Universität Bern
Bern
Switzerland
Ryan Blair
Department of Mathematics and Statistics
California State University, Long Beach
Long Beach, CA
United States
Alexandra Kjuchukova
Department of Mathematics
University of Notre Dame
Notre Dame, IN
United States
Filip Misev
Fakultät für Mathematik
Universität Regensburg
Regensburg
Germany

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