Torsion-freeness of ordered graph configuration spaces

Prove or refute the conjecture that ordered configuration spaces of graphs have torsion-free homology.

Background

The paper distinguishes ordered from unordered configuration spaces. It reports that torsion-freeness is conjectured for ordered configurations, but that the conjecture remains unresolved in nearly all cases.

References

In the case of ordered configurations, it is conjectured that there cannot be torsion, but it is not known in virtually all cases (See cite{hainaut2025representation} on the most up to date theorems about torsion in ordered configuration spaces of graphs).

— Universality in the algebra and topology of cographs  (2609.04554 - Mamun et al., 3 Sep 2026) in Section 5.1, subsection “Anchored configuration spaces of cographs”