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

Published online by Cambridge University Press:  28 November 2001

MORRIS W. HIRSCH  and
ALAN WEINSTEIN
MORRIS W. HIRSCH
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA (e-mail: [email protected])
ALAN WEINSTEIN
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA (e-mail: [email protected])
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Abstract

We show that every real analytic action of a connected supersoluble Lie group on a compact surface with non-zero Euler characteristic has a fixed point. This implies that 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 6 , December 2001 , pp. 1783 - 1787
Copyright
2001 Cambridge University Press

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