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This is a Quantitative Study study.

September 23, 2025Open Access

Modular systoles are extremal for the crossing number

Key Points

The study identifies that systoles exhibit extremal properties concerning the crossing number.
It demonstrates that intersection rates among congruence surfaces are optimally minimal for the given curves.
The analysis involves considering a family of curves that lie on the same topological surface to derive conclusions.
These findings suggest implications for understanding geometric configurations within topological spaces.

Abstract

We study crossing numbers for systoles of congruence surfaces. Taken as a family of curves on a family of surfaces, we show that the growth rate of their intersection is optimally small among all sets of curves of the same cardinality lying on the same topological surface.

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Burrin et al. (Thu,) studied this question.

synapsesocial.com/papers/68d475a031b076d99fa6df0c — DOI: https://doi.org/10.48550/arxiv.2508.20958

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Authors

Claire Burrin

University of Zurich

Hugo Parlier

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Modular systoles are extremal for the crossing number

Key Points

Abstract

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Discussion

Cite this study

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Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion

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