Given a stability condition defined over a category, every object in this category
is filtered by some distinguished objects called semistables. This
filtration, that is unique up-to-isomorphism, is know as the
One less studied property of stability conditions, when defined over an
abelian category, is the fact that each of them induce a chain of torsion
classes that is naturally indexed.
In this talk we will study arbitrary indexed chain of torsion classes. Our
first result states that every indexed chain of torsion classes induce a
Harder-Narasimhan filtration. Following ideas from Bridgeland we
show that the set of all indexed chains of torsion classes satisfying a mild
technical condition forms a topological space. If time we
will characterise the neighbourhood or some distinguished points.
- Algebra Seminar