Coxeter groups and meridional rank of links

Baader, Sebastian; Blair, Ryan; Kjuchukova, Alexandra

doi:10.1007/s00208-020-02124-z

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Coxeter groups and meridional rank of links

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Baader, Sebastian
Max Planck Institute for Mathematics, Max Planck Society;

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Kjuchukova, Alexandra
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s00208-020-02124-z
(Publisher version)

https://doi.org/10.48550/arXiv.1907.02982
(Preprint)

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Baader-Blair-Kjuchukova_Coxeter groups and meridional rank of links_2021.pdf
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Citation

Baader, S., Blair, R., & Kjuchukova, A. (2021). Coxeter groups and meridional rank of links. Mathematische Annalen, 379(3-4), 1533-1551. doi:10.1007/s00208-020-02124-z.

Cite as: https://hdl.handle.net/21.11116/0000-0007-D9FB-A

Abstract

We prove the meridional rank conjecture for twisted links and arborescent
links associated to bipartite trees with even weights. These links are
substantial generalizations of pretzels and two-bridge links, respectively.
Lower bounds on meridional rank are obtained via Coxeter quotients of the
groups of link complements. Matching upper bounds on bridge number are found
using the Wirtinger numbers of link diagrams, a combinatorial tool developed by
the authors.