Volume 7, issue 2 (2003)

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Area preserving group actions on surfaces

John Franks and Michael Handel

Geometry & Topology 7 (2003) 757–771
 arXiv: math.DS/0203159
Abstract

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

Keywords
group actions, Heisenberg group, almost simple
Primary: 57S25
Secondary: 37E30