An algebraic approach to Harder-Narasimhan filtrations

Abstract

In this article we study chains of torsion classes in an abelian category $\mathcal{A}$. We prove that chains of torsion classes induce a Harder-Narasimhan filtrations for every non-zero object $M$ in $\mathcal{A}$ and we characterise the slicings of $\mathcal{A}$ in terms of chain of torsion classes. Later, we show that all chain of torsion classes form a topological space and we study some of its properties. We finish the paper by showing that wall-crossing formulas can be deduced from chain of torsion classes.Comment: 31 pages. Added Section 8 and minor typos correcte