A sphere of spherical objects
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915499262083072 |
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| author | Bapat, Asilata Deopurkar, Anand Licata, Anthony M. |
| author_facet | Bapat, Asilata Deopurkar, Anand Licata, Anthony M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13912 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A sphere of spherical objects Bapat, Asilata Deopurkar, Anand Licata, Anthony M. Representation Theory Combinatorics 18G80, 05E45, 52C35, 20F36 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. |
| title | A sphere of spherical objects |
| topic | Representation Theory Combinatorics 18G80, 05E45, 52C35, 20F36 |
| url | https://arxiv.org/abs/2509.13912 |