Modular systoles are extremal for the crossing number
Geometric Topology
2025-08-29 v1 Combinatorics
Number Theory
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.
Cite
@article{arxiv.2508.20958,
title = {Modular systoles are extremal for the crossing number},
author = {Claire Burrin and Hugo Parlier},
journal= {arXiv preprint arXiv:2508.20958},
year = {2025}
}
Comments
7 pages