2022/08/05 by Nathan Broomhead, David Pauksztello, Broomhead, Nathan +5 · 3 citations
Mathematics · #14F08 #16E35 #18G80 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2208.03173
openalex publication_date 2022/08/05 · openalex created_date 2022/10/06 · openalex updated_date 2026/08/01
We introduce two extensions of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase. The subcategory of massless objects is thick and there is an induced Bridgeland stability on the quotient category. We study deformations of lax stability conditions. Second we consider the space arising by identifying lax stability conditions which are deformation-equivalent with fixed charge. This second space is stratified by stability spaces of Verdier quotients of the triangulated category by thick subcategories of massless objects. We illustrate our results through examples in which the Grothendieck group has rank 2. For these, our extended stability spaces can be explicitly described and related to the wall-and-chamber structure of the stability space.