Geometry & Topology, Vol. 7 (2003) Paper no. 21, pages 757--771.

Area preserving group actions on surfaces

John Franks, Michael Handel

Abstract. Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional integer Heisenberg group. For example any finite index subgroup of SL(3,Z) is such a group. The main result of this paper is that every action of G on a closed oriented surface by area preserving diffeomorphisms factors through a finite group.

Keywords. Group actions, Heisenberg group, almost simple

AMS subject classification. Primary: 57S25. Secondary: 37E30.

DOI: 10.2140/gt.2003.7.757

E-print: arXiv:math.DS/0203159

Submitted to GT on 28 March 2003. (Revised 26 October 2003.) Paper accepted 29 October 2003. Paper published 30 October 2003.

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John Franks, Michael Handel
Department of Mathematics, Northwestern University
Evanston, IL 60208-2730, USA
Department of Mathematics, CUNY, Lehman College
Bronx, NY 10468, USA


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