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arXiv · 2506.14943

Intersection numbers between horizontal foliations of quadratic differentials

Dragomir Saric·Taro Shima
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Abstract

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.

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Dragomir Saric, Taro Shima. 2025-06-17. Intersection numbers between horizontal foliations of quadratic differentials. https://arxiv.org/abs/2506.14943

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