Small non-Leighton two-complexes
Natalia S. Dergacheva, Anton A. Klyachko
TL;DR
This paper investigates the minimal conditions under which two finite CW-complexes with two-cells share an infinite common cover, providing an almost minimal example with two two-cells in each complex.
Contribution
It constructs an almost minimal example of two finite CW-complexes with two-cells that share an infinite common cover, extending Leighton's theorem.
Findings
Constructed an example with two two-cells in each complex
Demonstrated the existence of a common infinite cover
Extended understanding of covering properties in CW-complexes
Abstract
How many two-cells must two finite CW-complexes have to admit a common, but not finite common, covering? Leighton's theorem says that both complexes must have two-cells. We construct an almost (?) minimal example with two two-cells in each complex.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology