Volume 7, issue 2 (2003)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Area preserving group actions on surfaces

John Franks and Michael Handel

Geometry & Topology 7 (2003) 757–771

arXiv: math.DS/0203159

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, ) 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
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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