On the crossing number of arithmetic curve systems

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

Authors

Sebastian Baader (ORCID: https://orcid.org/0009-0007-4699-6682)
Luca Studer (ORCID: https://orcid.org/0000-0002-2079-8561)
Claire Burrin (ORCID: https://orcid.org/0000-0003-0036-5539)

Publication Details

Journal: Universität Zürich, ZORA
Published: 2025-11-24
DOI: https://doi.org/10.5167/uzh-281400
Primary Topic: Geometric and Algebraic Topology
Type: article
Field-Weighted Citation Impact: 0.00

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article

On the crossing number of arithmetic curve systems

Sebastian Baader, Luca Studer, Claire Burrin

Nov 24, 2025

Universität Zürich, ZORA

Geometric and Algebraic Topology

article

On the crossing number of arithmetic curve systems

Sebastian Baader, Luca Studer, Claire Burrin

November 24, 2025article en

Abstract

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

Universität Zürich, ZORA

Openalex Percentile: Top 17%

Geometric and Algebraic Topology

DOI Open Access PDF OpenAlex

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On the crossing number of arithmetic curve systems — Sebastian Baader, Luca Studer, et al. · Universität Zürich, ZORA (2025) | TGRS Research Map | TGRS