Algebraic & Geometric Topology

On periodic groups of homeomorphisms of the $2$–dimensional sphere

Jonathan Conejeros

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We prove that every finitely generated group of homeomorphisms of the 2 –dimensional sphere all of whose elements have a finite order which is a power of 2 and is such that there exists a uniform bound for the orders of the group elements is finite. We prove a similar result for groups of area-preserving homeomorphisms without the hypothesis that the orders of group elements are powers of 2 provided there is an element of even order.

Article information

Algebr. Geom. Topol., Volume 18, Number 7 (2018), 4093-4107.

Received: 1 December 2017
Revised: 7 June 2018
Accepted: 14 July 2018
First available in Project Euclid: 18 December 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F50: Periodic groups; locally finite groups 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 37E45: Rotation numbers and vectors 57S25: Groups acting on specific manifolds

Burnside problem surface homeomorphisms $2$–sphere


Conejeros, Jonathan. On periodic groups of homeomorphisms of the $2$–dimensional sphere. Algebr. Geom. Topol. 18 (2018), no. 7, 4093--4107. doi:10.2140/agt.2018.18.4093.

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