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Modular systoles are extremal for the crossing number
Claire Burrin, Hugo Parlier · 2025-08-29 · via math.CO updates on arXiv.org

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.