Diffeomorphism groups of tame Cantor sets and Thompson-like groups - Archive ouverte HAL
Article Dans Une Revue Compositio Mathematica Année : 2018

Diffeomorphism groups of tame Cantor sets and Thompson-like groups

Louis Funar

Résumé

The group of $\mathcal C^1$-diffeomorphisms of any sparse Cantor subset of a manifold is countable and discrete (possibly trivial). Thompson's groups come out of this construction when we consider central ternary Cantor subsets of an interval. Brin's higher dimensional generalizations $nV$ of Thompson's group $V$ arise when we consider products of central ternary Cantor sets. We derive that the $\mathcal C^2$-smooth mapping class group of a sparse Cantor sphere pair is a discrete countable group and produce this way versions of the braided Thompson groups.
Fichier principal
Vignette du fichier
1411.4855v4.pdf (616.97 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01992012 , version 1 (15-10-2024)

Identifiants

Citer

Louis Funar, Yurii Neretin. Diffeomorphism groups of tame Cantor sets and Thompson-like groups. Compositio Mathematica, 2018, 154 (05), pp.1066-1110. ⟨10.1112/S0010437X18007066⟩. ⟨hal-01992012⟩
21 Consultations
5 Téléchargements

Altmetric

Partager

More