Topology and dimension of the simplicial complex for arbitrary generic 2-CY categories

Determine whether the simplicial complex associated with a generic stability condition on an arbitrary 2-Calabi–Yau category is a manifold and, if so, determine its dimension.

Background

The paper constructs the simplicial complex from semistable spherical objects and HN filtrations and proves that, in type A and rank-two settings, the resulting complexes have strong topological structure. It asks whether analogous manifold properties persist for arbitrary 2-Calabi–Yau categories, including categories associated with more general graphs and geometric examples such as derived categories of coherent sheaves on K3 surfaces.