Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2206.09652 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- We establish some algebraic properties of the group $\mathrm{Diff}(\mathbb{C}^n,0)$ of germs of analytic diffeomorphisms of $\mathbb{C}^n$, and its formal completion $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$. For instance we describe the commutator of $\mathrm{Diff}(\mathbb{C}^n,0)$, but also prove that any finitely generated subgroup of $\mathrm{Diff}(\mathbb{C}^n,0)$ is residually finite; we thus obtain some constraints of groups that embed into $\mathrm{Diff}(\mathbb{C}^n,0)$. We show that $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$ is an Hopfian group, and that $\mathrm{Diff}(\mathbb{C}^n,0)$ and $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$ are not co-Hopfian. We end by the description of the automorphisms groups of $\widehat{\mathrm{Diff}}(\mathbb{C},0)$, and $\mathrm{Diff}(\mathbb{C},0)$.