The distribution of critical graphs of Jenkins-Strebel differentials
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912542184439808 |
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| author | Arana-Herrera, Francisco Calderon, Aaron |
| author_facet | Arana-Herrera, Francisco Calderon, Aaron |
| contents | By work of Jenkins and Strebel, given a Riemann surface X and a simple closed multi-curve $α$ on it, there exists a unique quadratic differential q on X whose horizontal foliation is measure equivalent to $α$. We study the distribution of the critical graphs of these differentials in the moduli space of metric ribbon graphs as the extremal length of the multi-curves goes to infinity, showing they equidistribute to the Kontsevich measure regardless of the initial choice of X. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01717 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The distribution of critical graphs of Jenkins-Strebel differentials Arana-Herrera, Francisco Calderon, Aaron Geometric Topology Dynamical Systems By work of Jenkins and Strebel, given a Riemann surface X and a simple closed multi-curve $α$ on it, there exists a unique quadratic differential q on X whose horizontal foliation is measure equivalent to $α$. We study the distribution of the critical graphs of these differentials in the moduli space of metric ribbon graphs as the extremal length of the multi-curves goes to infinity, showing they equidistribute to the Kontsevich measure regardless of the initial choice of X. |
| title | The distribution of critical graphs of Jenkins-Strebel differentials |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2305.01717 |