Fixed points of analytic actions of supersoluble Lie groups on compact surfaces

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We show that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima's fixed point free $C^{\infty}$ action on $S^2$ of the affine group of the line cannot be approximated by analytic actions. An example is given of an analytic, fixed point free action on $S^2$ of a solvable group that is not supersoluble.
6 pages, minor revisions in second verson

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Dynamical Systems, Geometric Topology, 58C30; 22E25

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http://salesiana.dossiersoluciones.com/handle/123456789/58612

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0002013
 http://arxiv.org/abs/math/0002013

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arXiv