Coxeter groups and meridional rank of links
Geometric Topology
2020-12-25 v2
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.
Cite
@article{arxiv.1907.02982,
title = {Coxeter groups and meridional rank of links},
author = {Sebastian Baader and Ryan Blair and Alexandra Kjuchukova},
journal= {arXiv preprint arXiv:1907.02982},
year = {2020}
}
Comments
18 pages, 9 figures, 2 footnotes. Cosmetic changes. Loss of one footnote. To appear in Math. Annalen