  A K3 category is by definition a Calabi-Yau category of dimension two.
Geometrically K3 categories occur as bounded derived categories of (twisted)
coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there
are no spherical objects (or just one up to shift). We study stability
conditions on K3 categories as introduced by Bridgeland and prove his
conjecture about the topology of the stability manifold and the
autoequivalences group for generic twisted projective K3, abelian surfaces, and
K3 surfaces with trivial Picard group.
