Article
On loxodromic actions of Artin–Tits groups
Author/s | Cumplido Cabello, María |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2018-04-10 |
Deposit Date | 2022-11-08 |
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Abstract | Artin–Tits groups act on a certain delta-hyperbolic complex, called the “additional length complex”. For an element of the group, acting loxodromically on this complex is a property analogous to the property of being ... Artin–Tits groups act on a certain delta-hyperbolic complex, called the “additional length complex”. For an element of the group, acting loxodromically on this complex is a property analogous to the property of being pseudo-Anosov for elements of mapping class groups. By analogy with a well-known conjecture about mapping class groups, we conjecture that “most” elements of Artin–Tits groups act loxodromically. More precisely, in the Cayley graph of a subgroup G of an Artin–Tits group, the proportion of loxodromically acting elements in a ball of large radius should tend to one as the radius tends to infinity. In this paper, we give a condition guaranteeing that this proportion stays away from zero. This condition is satisfied e.g. for Artin–Tits groups of spherical type, their pure subgroups and some of their commutator subgroups. |
Citation | Cumplido Cabello, M. (2018). On loxodromic actions of Artin–Tits groups. Journal of pure and applied algebra, 223 (1), 340-348. https://doi.org/10.1016/j.jpaa.2018.03.013. |
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