On manifolds with nonhomogeneous factors

TL;DR

This paper provides simple examples of finite-dimensional connected homogeneous manifolds with nonhomogeneous factors, addressing an old problem in topology and illustrating the complexity of homogeneous spaces.

Contribution

It introduces elementary examples of homogeneous manifolds with nonhomogeneous factors, solving a longstanding open problem in the field.

Findings

Existence of finite-dimensional connected homogeneous spaces with nonhomogeneous factors

Elementary solutions to classical problems in topology

Illustration of nonrigid structures in homogeneous manifolds

Abstract

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general topology concerning homogeneous spaces.