Integral torsion in anchored configuration spaces

Determine whether anchored configuration spaces of graphs can have integral torsion in their homology groups.

Background

Anchored configuration spaces allow configured points to collide and require specified anchor vertices to occur among the points. The paper states that torsion-freeness is known for anchored configuration spaces of trees and cycles, but that insufficient computations exist beyond those cases to resolve whether integral torsion can occur in general.

References

To date, it is not known whether or not anchored configuration spaces can admit integral 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”