## Algebraic & Geometric Topology

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

Jonathan Conejeros

#### Abstract

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

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

Dates
Revised: 7 June 2018
Accepted: 14 July 2018
First available in Project Euclid: 18 December 2018

https://projecteuclid.org/euclid.agt/1545102065

Digital Object Identifier
doi:10.2140/agt.2018.18.4093

Mathematical Reviews number (MathSciNet)
MR3892240

Zentralblatt MATH identifier
07006386

#### Citation

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. https://projecteuclid.org/euclid.agt/1545102065

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