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Feuilles compactes d’un feuilletage générique en codimension $1$

Christian Bonatti; Sebastião Firmo — 1994

Annales scientifiques de l'École Normale Supérieure

Fixed points of discrete nilpotent group actions on $S^{2}$

Suely Druck; Fuquan Fang; Sebastião Firmo — 2002

Annales de l’institut Fourier

We prove that for each integer $k \geq 2$ there is an open neighborhood $𝒱_{k}$ of the identity map of the 2-sphere $S^{2}$ , in $C^{1}$ topology such that: if $G$ is a nilpotent subgroup of ${Diff}^{1} (S^{2})$ with length $k$ of nilpotency, generated by elements in $𝒱_{k}$ , then the natural $G$ -action on $S^{2}$ has nonempty fixed point set. Moreover, the $G$ -action has at least two fixed points if the action has a finite nontrivial orbit.

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Feuilles compactes d’un feuilletage générique en codimension 1

Fixed points of discrete nilpotent group actions on S 2

Feuilles compactes d’un feuilletage générique en codimension $1$

Fixed points of discrete nilpotent group actions on $S^{2}$