Forester's lattices and small non-Leighton complexes

TL;DR

This paper constructs two CW-complexes with a shared, but not finitely shared, covering space, highlighting complex relationships in topological coverings and cell structures.

Contribution

It introduces two CW-complexes with a common infinite covering but no finite common covering, advancing understanding of complex topological coverings.

Findings

Constructed CW-complexes with a common infinite cover

Demonstrated the absence of finite common covers for these complexes

Provided examples relevant to topological and algebraic properties of complexes

Abstract

We construct two CW-complexes $K$ and $L$ admitting a common, but not finite common, covering, where $K$ is homeomorphic to a complex with a single 2-cell.