On the crossing number of arithmetic curve systems

Key Points

• The research aims to determine the crossing number of systoles in hyperbolic surfaces related to congruence lattices.
• Analyzed the properties of systoles in hyperbolic surfaces
• Investigated the relationship with congruence lattices in SL2(Z)
• Established connections between asymptotic behavior and crossing numbers
• Demonstrated that the family of systoles has asymptotically minimal crossing numbers
• Provided evidence supporting the geometric implications of these findings