Modular systoles are extremal for the crossing number

2025/08/28 by Burrin, Claire, Parlier, Hugo
#Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.20958

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.

Citations

• Crossing number inequalities for curves on surfaces
• On the crossing number of arithmetic curve systems

Related

• On the crossing number of arithmetic curve systems
• Small filling sets of curves on a surface
• Crossing number inequalities for curves on surfaces
• Crossing number of curves on surfaces
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