Spherical objects and stability conditions on 2-Calabi--Yau quiver categories

2021/08/20 by Asilata Bapat, Bapat, Asilata, Anand Deopurkar +3 · 3 citations
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2108.09155

Abstract

Consider a 2-Calabi--Yau triangulated category with a Bridgeland stability condition. We devise an effective procedure to reduce the phase spread of an object by applying spherical twists. Using this, we give new proofs of the following theorems for 2-Calabi--Yau categories associated to ADE quivers: (1) all spherical objects lie in a single orbit of the braid group, and (2) the space of Bridgeland stability conditions is connected.

Cited by

• Extriangulated structures from stability conditions and application to braid representations
• A sphere of spherical objects
• Spherical and Semibrick Classifications

Related

• A sphere of spherical objects
• Remarks on the Bondal quiver
• Correspondence between 2 Calabi-Yau Categories and Quivers
• q-deformed rational numbers and the 2-Calabi--Yau category of type A₂
• Stability conditions on CY_N categories associated to A_n-quivers and period maps