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
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.

Keywords
Burnside problem, surface homeomorphisms, $2$–sphere
Mathematical Subject Classification 2010
Primary: 20F50, 37B05, 37E30, 37E45, 57S25