A quotient of the stability manifold by an equivalence relation is a real manifold of half dimension, and the original manifold can be reconstructed from the quotient together with the relation ≲.
Stability Manifold of P^1
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abstract
T. Bridgeland defined the notion of a stability manifold for a triangulated category, motivated by Douglas's work on \Pi-stability for D-branes. We show that the stability manifold of the bounded derived category of the coherent sheaves on P^1 is C^2. This is the first complete picture of a stability manifold for a non-Calabi-Yau manifold.
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A Real Reduction of the Manifold of Bridgeland Stability Conditions
A quotient of the stability manifold by an equivalence relation is a real manifold of half dimension, and the original manifold can be reconstructed from the quotient together with the relation ≲.