Perfection uniforme pour les échanges d'intervalles avec ou sans retournements

Guelman, Nancy; Liousse, Isabelle

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.5802/aif.3502

Title :

Perfection uniforme pour les échanges d'intervalles avec ou sans retournements

Author(s) :

Guelman, Nancy [Auteur]
Liousse, Isabelle [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Annales de l'Institut Fourier

Pages :

1477-1501

Publisher :

Association des Annales de l'Institut Fourier

Publication date :

2022-09-12

ISSN :

0373-0956

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Let G be the group of all Interval Exchange Transformations. Results of Arnoux-Fathi ([Arn81b]), Sah ([Sah81]) and Vorobets ([Vor17]) state that G 0 the subgroup of G generated by its commutators is simple. In ([Arn81b]), ...
Show more >Let G be the group of all Interval Exchange Transformations. Results of Arnoux-Fathi ([Arn81b]), Sah ([Sah81]) and Vorobets ([Vor17]) state that G 0 the subgroup of G generated by its commutators is simple. In ([Arn81b]), Arnoux proved that the group G of all Interval Exchange Transformations with flips is simple. We establish that every element of G has a commutator length not exceeding 6. Moreover, we give conditions on G that guarantee that the commutator lengths of the elements of G 0 are uniformly bounded, and in this case for any g ∈ G 0 this length is at most 5. As analogous arguments work for the involution length in G, we add an appendix whose purpose is to prove that every element of G has an involution length not exceeding 12.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 :