Another homogeneous, non-bihomogeneous Peano continuum

TL;DR

This paper presents a simpler example of a homogeneous, finite-dimensional continuum that is not bihomogeneous, using a novel approach involving fundamental groups with non-conjugate elements.

Contribution

It introduces a new, simpler construction of a homogeneous but not bihomogeneous continuum, expanding understanding of such topological spaces.

Findings

Provides a new example of a homogeneous, finite-dimensional continuum

Uses a fundamental group with non-conjugate elements to distinguish properties

Simplifies previous complex constructions in the field

Abstract

K. Kuperberg found a locally connected, finite-dimensional continuum which is homogeneous but not bihomogeneous. We give a similar but simpler example. Like previous constructions, the example is locally a Cartesian product of Menger spaces. The new idea is to choose a fundamental group in which not every element is conjugate to its inverse.