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- W2691309097 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." @default.
- W2691309097 created "2017-06-30" @default.
- W2691309097 creator A5085115187 @default.
- W2691309097 date "2017-06-26" @default.
- W2691309097 modified "2023-09-27" @default.
- W2691309097 title "On the loxodromic actions of Artin-Tits groups" @default.
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