A characterization of alternating link exteriors in terms of cubed complexes

TL;DR

This paper characterizes alternating link exteriors using cubed complexes, introducing the concept of signed BW cubed-complexes to identify when such complexes correspond to these link exteriors.

Contribution

It introduces the concept of signed BW cubed-complexes and provides a characterization criterion for when these complexes represent alternating link exteriors.

Findings

Signed BW cubed-complexes can be used to identify alternating link exteriors.

A new topological characterization of alternating link exteriors.

Framework for analyzing link exteriors via cubed complexes.

Abstract

We give a characterization of alternating link exteriors in terms of cubed complexes. To this end, we introduce the concept of a "signed BW cubed-complex", and give a characterization for a signed BW cubed-complex to have the underlying space which is homeomorphic to an alternating link exterior.