Stability conditions for derived categories
The notion of stability condition on a triangulated category has been introduced by Bridgeland in , following ideas from physics by Douglas  on π-stability for D-branes. A stability condition on a triangulated category ℑ is given by abstracting the usual properties of μ-stability for sheaves on complex projective varieties; one introduces the notion of slope, using a group homomorphism from the Grothendieck group K(ℑ) of ℑ to ℂ, and requires that a stability condition has generalized Harder-Narasimhan filtrations and is compatible with the shift functor. The main property is that there exists a parameter space Stab(ℑ) for stability conditions, endowed with a natural topology, which is a (possibly infinitedimensional) complex manifold. The space of stability conditions Stab(ℑ) thus yields a geometric invariant naturally attached to a triangulated category ℑ.
KeywordsStability Condition Modulus Space Stability Function Abelian Category Triangulate Category
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