Geometry & Topology

Area preserving group actions on surfaces

John Franks and Michael Handel

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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.

Article information

Geom. Topol., Volume 7, Number 2 (2003), 757-771.

Received: 28 March 2003
Revised: 26 October 2003
Accepted: 29 October 2003
First available in Project Euclid: 21 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57S25: Groups acting on specific manifolds
Secondary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces

group actions Heisenberg group almost simple


Franks, John; Handel, Michael. Area preserving group actions on surfaces. Geom. Topol. 7 (2003), no. 2, 757--771. doi:10.2140/gt.2003.7.757.

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