Weak stability conditions and the space of chains of torsion classes

2023/06/14 by Aran Tattar, Hipolito Treffinger, Tattar, Aran +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #18E10 #18E40 #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Microtubule and mitosis dynamics #Protein Tyrosine Phosphatases #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2306.08589

openalex publication_date 2023/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show an explicit relation between chains of torsion classes and weak stability conditions over an abelian category. In particular, up to a natural equivalence, they coincide. We investigate topological properties of the space of chains of torsion classes and its quotient given by this equivalence relation. In particular we show that this space is compact if and only if the abelian category has finitely many torsion classes.

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