ALGEBRAIC PROPERTIES OF THE GROUP OF GERMS OF DIFFEOMORPHISMS
Résumé
We establish some algebraic properties of the group Diff(C^n ,0) of germs of analytic diffeomorphisms of C^n, and its formal completion $\widehat{Diff}(C^n ,0)$. For instance we describe the commutator of Diff(C^n ,0), but also prove that any finitely generated subgroup of Diff(C^n,0) is residually finite; we thus obtain some constraints of groups that embed into Diff(C^n ,0). We show that Diff(C^n,0) is an Hopfian group, and that Diff(C^n,0) and $\widehat{Diff}(C^n ,0)$ are not co-Hopfian. We end by the description of the automorphisms groups of $\widehat{Diff}(C^n ,0)$, and Diff(C, 0).
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|