Wall-crossing formulas via spectral networks
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913984250118144 |
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| author | Horn, Johannes Möller, Martin |
| author_facet | Horn, Johannes Möller, Martin |
| contents | We give a self-contained proof of the Kontsevich-Soibelman wall-crossing formula entirely in the scope of quadratic differentials without relying on input from DT theory. Our approach is based on path-lifting rules for spectral networks introduced by Gaiotto, Moore and Neitzke. We provide a framework to justify the convergence of the path liftings, including the cases with spiral domains. In particular, we define path lifting rules for spectral networks associated to holomorphic quadratic differentials. As an intermediate step in the proof of the wall-crossing formula, we show that upon extending the path lifting rules to $\mathcal{A}_0$-laminations we generate the hat-homology lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wall-crossing formulas via spectral networks Horn, Johannes Möller, Martin Algebraic Geometry Geometric Topology We give a self-contained proof of the Kontsevich-Soibelman wall-crossing formula entirely in the scope of quadratic differentials without relying on input from DT theory. Our approach is based on path-lifting rules for spectral networks introduced by Gaiotto, Moore and Neitzke. We provide a framework to justify the convergence of the path liftings, including the cases with spiral domains. In particular, we define path lifting rules for spectral networks associated to holomorphic quadratic differentials. As an intermediate step in the proof of the wall-crossing formula, we show that upon extending the path lifting rules to $\mathcal{A}_0$-laminations we generate the hat-homology lattice. |
| title | Wall-crossing formulas via spectral networks |
| topic | Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2508.07727 |