SPHERICAL OBJECTS AND STABILITY CONDITIONS ON CY2 QUIVER CATEGORIES

Let C be a triangulated category. Suppose C admits a Bridgeland stability condition τ . We can use τ to endow C with a rich array of additional structures. These structures can be of a geometric flavour, such as a measure of the mass or the spread of every object, a measure of length of every morphism, or of a combinatorial flavour, such as the counts of multiplicities of semi-stable objects in the Harder–Narasimhan filtration. These additional structure gives new tools to understand old questions about C. We apply this philosophy to study the 2-Calabi–Yau category CΓ associated a quiver Γ. As an application, when Γ is of finite type, we obtain a classification of all spherical objects in CΓ. Theorem 1.1. Let Γ be a quiver of type An, Dn, or E6, E7, E8. The spherical objects of CΓ lie in the BΓ orbit of the simple objects of the standard heart.