Area preserving group actions on surfaces

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 $S L (3, ℤ)$ 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

Mathematical Subject Classification 2000

Primary: 57S25

Secondary: 37E30

References

Forward citations

Publication

Received: 28 March 2003

Revised: 26 October 2003

Accepted: 29 October 2003

Published: 30 October 2003

Proposed: Benson Farb

Seconded: Leonid Polterovich, Joan Birman

Authors

John Franks
Department of Mathematics Northwestern University Evanston Illinois 60208-2730 USA

Michael Handel
Department of Mathematics CUNY, Lehman College Bronx New York 10468 USA

Volume 7, issue 2 (2003)

John Franks and Michael Handel