A note on fixed points of abelian actions in dimension one

TL;DR

This paper discusses a 1-dimensional continuum arising from Boyce and Huneke's result, showing it admits two commuting homeomorphisms with no common fixed point, highlighting interesting fixed point properties in dimension one.

Contribution

It provides a new example of a 1-dimensional continuum with commuting homeomorphisms lacking a common fixed point, expanding understanding of fixed point phenomena in dimension one.

Findings

Constructs a 1-dimensional continuum from a family of disks

Shows existence of two commuting homeomorphisms without common fixed points

Highlights fixed point properties in low-dimensional continua

Abstract

The result of Boyce and Huneke gives rise to a 1-dimensional continuum, which is the intersection of a descending family of disks, that admits two commuting homeomorphisms without a common fixed point.