The pure-EKR conjecture for flag simplicial manifolds

A simplicial complex is pure-EKR if its facets have the Erdős–Ko–Rado property: every intersecting family of facets has at most the size of the star of some vertex. A simplicial complex is a simplicial manifold when its underlying space is homeomorphic to a closed manifold, and it is flag when every set of vertices that pairwise span edges forms a face.

Flag-manifold conjecture. Every flag simplicial manifold is pure-EKR.

This is a special case of the conjecture for pure flag complexes without boundary. The paper presents it as an important geometric special case, but does not resolve it in general.