Constraints on stable factors in HN filtrations

Characterize the constraints on collections of stable spherical objects that can occur together in the Harder–Narasimhan filtration of a spherical object for a generic stability condition on a 2-Calabi–Yau category.

Background

Understanding which stable spherical objects may occur simultaneously as HN factors is identified as central to determining the combinatorial and topological structure of the simplicial complex. In type A, these constraints are described geometrically through pointed pseudo-triangulations; the paper asks for an analogous characterization in general 2-Calabi–Yau categories.