A sphere of spherical objects
Representation Theory
2025-09-18 v1 Combinatorics
Abstract
Given a Bridgeland stability condition on a 2-Calabi--Yau category, we define a simplicial complex that encodes the Harder--Narasimhan filtrations of spherical objects. For 2-Calabi--Yau categories of type A, we relate this complex to the complex of pointed pseudo-triangulations on configurations of points on the plane. Using this connection, we prove that the complex undergoes piecewise-linear wall-crossings as we vary the stability condition, and is piecewise-linearly homeomorphic to a sphere. Additionally, we prove that for a generic stability condition on a 2-Calabi--Yau category, a spherical object is determined by the ordered list of its Harder--Narasimhan factors.
Cite
@article{arxiv.2509.13912,
title = {A sphere of spherical objects},
author = {Asilata Bapat and Anand Deopurkar and Anthony M. Licata},
journal= {arXiv preprint arXiv:2509.13912},
year = {2025}
}