Title :

INTERVAL EXCHANGE TRANSFORMATIONS GROUPS : FREE ACTIONS AND DYNAMICS OF VIRTUALLY ABELIAN GROUPS

Author(s) :

Guelman, Nancy [Auteur]
Liousse, Isabelle [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Publication date :

2024-03-02

English keyword(s) :

2020 Mathematics Subject Classification. 37E05 57S30 37C85 20K35 20F50 Interval exchange transformations virtually abelian groups free actions dynamical classification
2020 Mathematics Subject Classification. 37E05
57S30
37C85
20K35
20F50 Interval exchange transformations
virtually abelian groups
free actions
dynamical classification

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

In this paper, we study groups acting freely by IETs. We first note that a finitely generated group admits a free IET action if and only if it is virtually abelian. Then, we classify the free actions of non virtually cyclic ...
Show more >In this paper, we study groups acting freely by IETs. We first note that a finitely generated group admits a free IET action if and only if it is virtually abelian. Then, we classify the free actions of non virtually cyclic groups showing that they are "conjugate" to actions in some specific subgroups G n , namely G n ≃ (G 2) n ⋊ S n where G 2 is the group of circular rotations seen as exchanges of 2 intervals and S n is the group of permutations of {1, ..., n} acting by permuting the copies of G 2. We also study non free actions of virtually abelian groups and we obtain the same conclusion for any such group that contains a conjugate to a product of restricted rotations with disjoint supports and without periodic points. As a consequence, we get that the group generated by f ∈ G n periodic point free and g / ∈ G n is not virtually nilpotent. Moreover, we exhibit examples of finitely generated non virtually nilpotent subgroups of IETs, some of them are metabelian and others are not virtually solvable.Show less >

Language :

Anglais

ANR Project :

Groupes d'homéomorphismes de variétés
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL