Title :

Simplicité uniforme pour les sous-groupes de bijections continues par morceaux de l'intervalle

Author(s) :

Guelman, Nancy [Auteur]
Liousse, Isabelle [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Arnoux, Pierre [Auteur]
Institut de Mathématiques de Marseille [I2M]

Journal title :

Bulletin of the London Mathematical Society

Publisher :

London Mathematical Society

Publication date :

2023

ISSN :

0024-6093

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Let I = [0, 1) and PC(I) [resp. PC + (I)] be the quotient group of the group of all piecewise continuous [resp. piecewise continuous and orientation preserving] bijections of I by its normal subgroup consisting in elements ...
Show more >Let I = [0, 1) and PC(I) [resp. PC + (I)] be the quotient group of the group of all piecewise continuous [resp. piecewise continuous and orientation preserving] bijections of I by its normal subgroup consisting in elements with finite support (i.e. that are trivial except at possibly finitely many points). Arnoux's thesis states that PC + (I) and certain groups of interval exchanges are simple, and the proofs of these results are the purpose of the Appendix. We prove the simplicity of the group A + (I) of locally orientation preserving, piecewise continuous, piecewise affine maps of the unit interval. These results can be improved. Indeed, a group G is uniformly simple if there exists a positive integer N such that for any f, ϕ ∈ G \ {Id}, the element ϕ can be written as a product of at most N conjugates of f or f −1. We provide conditions which guarantee that a subgroup G of PC(I) is uniformly simple. As corollaries, we obtain that PC(I), PC + (I), PL + (S 1), A(I), A + (I) and some Thompson like groups included the Thompson group T are uniformly simple.Show less >

Language :

Anglais

Popular science :

Non

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