2025/09/17 by Asilata Bapat, Bapat, Asilata, Anand Deopurkar +3 · 1 citation
Mathematics · #05E45 #18G80 #20F36 #52C35 #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2509.13912
openalex publication_date 2025/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.