Titre :

REVERSIBLE MAPS AND PRODUCTS OF INVOLUTIONS IN GROUPS OF IETS

Auteur(s) :

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

Discipline(s) HAL :

Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Théorie des groupes [math.GR]

Résumé en anglais : [en]

An element f of a group G is reversible if it is conjugated in G to its own inverse; when the conjugating map is an involution, f is called strongly reversible. We describe reversible maps in certain groups of interval ...
Lire la suite >An element f of a group G is reversible if it is conjugated in G to its own inverse; when the conjugating map is an involution, f is called strongly reversible. We describe reversible maps in certain groups of interval exchange transformations namely Gn ≃ (S 1) n ⋊ Sn, where S 1 is the circle and Sn is the group of permutations of {1, ..., n}. We first characterize strongly reversible maps, then we show that reversible elements are strongly reversible. As a corollary, we obtain that composites of involutions in Gn are product of at most four involutions. We prove that any reversible Interval Exchange Transformation (IET) is reversible by a finite order element and then it is the product of two periodic IETs. In the course of proving this statement, we classify the free actions of BS(1, −1) by IET and we extend this classification to free actions of finitely generated torsion free groups containing a copy of Z 2. We also give examples of faithful free actions of BS(1, −1) and other groups containing reversible IETs. We show that periodic IETs are product of at most 2 involutions. For IETs that are products of involutions, we show that such 3-IETs are periodic and then are product of at most 2 involutions and we exhibit a family of non periodic 4-IETs for which we prove that this number is at least 3 and at most 6.Lire moins >

Langue :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T17:10:37Z