Stability condition

Summary

A stability condition on a triangulated category is a pair made of a central charge and a slicing. The central charge is a homomorphism from the Grothendieck group to $\C$. The slicing assigns to each real number a class of semistable objects of that phase. The notion was introduced by Tom Bridgeland to give a uniform meaning to stability of sheaves and of quiver representations. The stability conditions on a fixed category form a space with a natural topology. The study of this space links algebraic geometry with string theory and mirror symmetry.