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Preprints, Working Papers, ... Year : 2022

ALGEBRAIC PROPERTIES OF THE GROUP OF GERMS OF DIFFEOMORPHISMS

Abstract

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).
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Dates and versions

hal-03725182 , version 1 (15-07-2022)

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  • HAL Id : hal-03725182 , version 1

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Dominique Cerveau, Julie Déserti. ALGEBRAIC PROPERTIES OF THE GROUP OF GERMS OF DIFFEOMORPHISMS. 2022. ⟨hal-03725182⟩
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