# On the loxodromic actions of Artin-Tits groups

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 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.
Type de document :
Article dans une revue
Journal of Pure and Applied Algebra, Elsevier, 2019, 223 (1), pp.340-348. 〈10.1016/j.jpaa.2018.03.013〉
Domaine :

https://hal.archives-ouvertes.fr/hal-01686721
Contributeur : Dominique Hervé <>
Soumis le : mercredi 17 janvier 2018 - 16:31:12
Dernière modification le : jeudi 15 novembre 2018 - 11:56:48

### Citation

María Cumplido Cabello. On the loxodromic actions of Artin-Tits groups. Journal of Pure and Applied Algebra, Elsevier, 2019, 223 (1), pp.340-348. 〈10.1016/j.jpaa.2018.03.013〉. 〈hal-01686721〉

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