Intersection numbers between horizontal foliations of quadratic differentials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908411387445248 |
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| author | Saric, Dragomir Shima, Taro |
| author_facet | Saric, Dragomir Shima, Taro |
| contents | We establish that the intersection number between the horizontal foliations of any two finite-area holomorphic quadratic differentials on an arbitrary Riemann surface is finite. Our main result shows that the intersection number is jointly continuous in the $L^1$-norm on the quadratic differentials. A corollary is that the Jenkins-Strebel differentials are not dense in the space of all finite-area holomorphic quadratic differentials when the infinite Riemann surface is not parabolic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersection numbers between horizontal foliations of quadratic differentials Saric, Dragomir Shima, Taro Complex Variables Dynamical Systems Geometric Topology We establish that the intersection number between the horizontal foliations of any two finite-area holomorphic quadratic differentials on an arbitrary Riemann surface is finite. Our main result shows that the intersection number is jointly continuous in the $L^1$-norm on the quadratic differentials. A corollary is that the Jenkins-Strebel differentials are not dense in the space of all finite-area holomorphic quadratic differentials when the infinite Riemann surface is not parabolic. |
| title | Intersection numbers between horizontal foliations of quadratic differentials |
| topic | Complex Variables Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2506.14943 |