Odd torsion in graph configuration-space homology

Determine whether odd torsion can occur in the homology groups of graph configuration spaces.

Background

The existence of odd torsion is identified as a major unresolved question for graph configuration spaces. The issue concerns integral homology and is presented as distinct from the more specific question of torsion in higher homological degrees.

References

In fact, arguably the most significant outstanding question in the theory of graph configuration spaces is whether or not it is possible for there to ever be odd torsion in their homology groups.

— 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”