Periodic points for amenable group actions on uniquely arcwise connected continua

TL;DR

This paper proves that for countable amenable groups acting on uniquely arcwise connected continua, there must be either a fixed point or a 2-periodic point, extending understanding of group actions on such spaces.

Contribution

It establishes a new fixed point or 2-periodic point existence result for amenable group actions on uniquely arcwise connected continua.

Findings

Existence of fixed or 2-periodic points for group actions

Extension of fixed point theorems to uniquely arcwise connected continua

Applicable to countable amenable groups

Abstract

We show that if $G$ is a countable amenable group acting on a uniquely arcwise connected continuum $X$, then $G$ has either a fixed point or a 2-periodic point in $X$.