Spherical objects and stability conditions on 2-Calabi--Yau quiver categories
Asilata Bapat, Anand Deopurkar, Anthony M. Licata
TL;DR
This paper introduces a method using spherical twists to analyze stability conditions in 2-Calabi--Yau categories, proving connectedness of the stability space and orbit properties of spherical objects for ADE quivers.
Contribution
It provides a new procedure to control phase spread via spherical twists and offers simplified proofs of key properties of stability conditions in 2-Calabi--Yau categories.
Findings
All spherical objects are in a single braid group orbit.
The space of Bridgeland stability conditions is connected.
New proof techniques for properties of 2-Calabi--Yau categories.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry