微分同胚germ的代数性质
Algebraic properties of the group of germs of diffeomorphisms
AI总结：
研究微分同胚germ群Diff(C^n,0)及其形式完备化群的代数性质，证明其交换子、余有限性及Hopfian性质，探讨嵌入该群的群结构约束。
摘要：
我们建立了微分同胚germ群Diff(C^n,0)及其形式完备化群widehat{Diff}(C^n,0)的某些代数性质。例如，我们描述了Diff(C^n,0)的交换子，证明了其任何有限生成子群都是余有限的；因此获得了一些嵌入Diff(C^n,0)的群的约束。我们显示widehat{Diff}(C^n,0)是一个Hopfian群，而Diff(C^n,0)和widehat{Diff}(C^n,0)不是co-Hopfian。最后描述了widehat{Diff}(C,0)和Diff(C,0)的自同构群。
英文摘要：
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 $\mathrm{Diff}(\mathbb{C},0)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
