Abstract:
Bridgeland assigned to any triangulated category a complex manifold: the space of stability conditions on it. In a joint work with Katzarkov we prove that the Bridgeland stability spaces on wild Kronecker quivers are CxH and these calculations suggest a new notion of a norm. To a triangulated category T which has property of a phase gap, we attach a number ||T||_epsilon \in [0,(1-epsilon)\pi] depending on a parameter epsilon \in (0,1). In this talk, I will tell more about this. In particular I plan to define and discuss a topology on a class of triangulated categories (categories with a phase gap). By non-commutative projective spaces I mean those introduced by Kontsevich-Rosenberg.