Holonomy representation of quasi-projective leaves of codimension one foliations

Claudon, Benoît; Loray, Frank; Pereira, Jorge Vitorio; Touzet, Frédéric

doi:10.5565/publmat6311910

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Residually Finite Groups1

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2022

2024

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Cited by 2 publications

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“…The following statement, that is mentioned in [CLPT19] without detail in the 1-dimensional and formal case, is a direct consequence of Theorem 3.2: Theorem 3.4. Any finitely generated subgroup of G n 0 (resp.…”

Section: Residually Finite Groupsmentioning

confidence: 91%

Algebraic properties of the group of germs of diffeomorphisms

Cerveau¹,

Déserti²

2022

Preprint

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We establish some algebraic properties of the group Diff(C n , 0) of germs of analytic diffeomorphisms of C n , and its formal completion 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 Diff(C n , 0) are not co-Hopfian. We end by the description of the automorphisms groups of Diff(C, 0), and Diff(C, 0).

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Section: Residually Finite Groupsmentioning

confidence: 91%