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

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...

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Bapat, Asilata, Deopurkar, Anand, Licata, Anthony M
Format: Article
Language:English
Subjects:
Braid theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422