Volume 18, issue 7 (2018)

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

Jonathan Conejeros

Algebraic & Geometric Topology 18 (2018) 4093–4107

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.

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Burnside problem, surface homeomorphisms, $2$–sphere
Mathematical Subject Classification 2010
Primary: 20F50, 37B05, 37E30, 37E45, 57S25
Received: 1 December 2017
Revised: 7 June 2018
Accepted: 14 July 2018
Published: 11 December 2018
Jonathan Conejeros
Departamento de Matemática y Ciencia de la Computación
Universidad de Santiago de Chile