Spherical objects and stability conditions on 2-Calabi–Yau quiver categories

We study actions of spherical twists on 2-Calabi–Yau categories with a Bridgeland stability condition. In these categories, we describe how to reduce the phase spread of a spherical object using stable spherical twists. In 2-Calabi–Yau quiver categories, we describe how to construct all spherical stable objects by applying simple spherical twists to the simple objects. As an application of this idea, we prove that for 2-Calabi–Yau categories associated to ADE quivers, all spherical objects lie in the braid group orbit of a simple object. We also give a new proof of the fact that the space of Bridgeland stability conditions is connected for these categories.