On the crossing number of arithmetic curve systems

Sebastian Baader; Claire Burrin; Luca Studer

doi:10.4171/cmh/609

JournalscmhVol. 101, No. 4pp. 755–763

On the crossing number of arithmetic curve systems

Sebastian Baader
Universität Bern, Switzerland
Claire Burrin
Universität Zürich, Switzerland
Luca Studer
Berner Fachhochschule, Biel, Switzerland

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Abstract

We show that the family of systoles of hyperbolic surfaces associated with congruence lattices in $SL_{2} (Z)$ have asymptotically minimal crossing number.

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Sebastian Baader, Claire Burrin, Luca Studer, On the crossing number of arithmetic curve systems. Comment. Math. Helv. 101 (2026), no. 4, pp. 755–763

DOI 10.4171/CMH/609