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On the crossing number of arithmetic curve systems

Geometric Topology 2024-03-11 v1 Number Theory

Abstract

We show that the family of systoles of hyperbolic surfaces associated with congruence lattices in SL2(Z)\mathrm{SL}_2(\mathbb{Z}) have asymptotically minimal crossing number.

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Cite

@article{arxiv.2403.05194,
  title  = {On the crossing number of arithmetic curve systems},
  author = {Sebastian Baader and Claire Burrin and Luca Studer},
  journal= {arXiv preprint arXiv:2403.05194},
  year   = {2024}
}

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8 pages