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November 24, 2025Open Access

On the crossing number of arithmetic curve systems

Sebastian Baader Claire Burrin Ben Luca Studer

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Key Points

The research aims to determine the crossing number of systoles in hyperbolic surfaces related to congruence lattices.
Analyzed the properties of systoles in hyperbolic surfaces
Investigated the relationship with congruence lattices in SL2(Z)
Established connections between asymptotic behavior and crossing numbers
Demonstrated that the family of systoles has asymptotically minimal crossing numbers
Provided evidence supporting the geometric implications of these findings

Implication

This analysis shows minimal crossing number in systoles of hyperbolic surfaces, suggesting significant implications for geometry.

Abstract

We show that the family of systoles of hyperbolic surfaces associated with congruence lattices in SL2(Z) have asymptotically minimal crossing number.

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Cite This Study

Baader et al. (2025) studied this question.

synapsesocial.com/papers/698586238f7c464f2300a03e https://doi.org/10.24451/arbor.12970

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Keep reading

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1On the crossing number of arithmetic curve systems2024
2Modular systoles are extremal for the crossing number2025
3Crossing number of curves on surfaces2024
4Systems of curves on non-orientable surfaces2024
5The rank of syzygies of canonical curves2024

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