Area preserving group actions on surfaces

Franks, John¹ ; Handel, Michael²

¹ Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730, USA
² Department of Mathematics, CUNY, Lehman College, Bronx, New York 10468, USA

Geometry & topology, Tome 7 (2003) no. 2, pp. 757-771.

Résumé

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

Détail

DOI : 10.2140/gt.2003.7.757

Keywords: group actions, Heisenberg group, almost simple

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