4 papers · 1 filter
The crossing number of polynomial curve systems
Sebastian Baader, Jasmin Jörg, Hugo Parlier
We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.
Sparse curve systems have intermediate growth type
Sebastian Baader, Jasmin Jörg, Danica Kosanović
A system of simple closed curves on a surface of genus is said to be sparse if their average pairwise intersection number does not exceed one. We show that the maximal size of…
Systoles on punctured spheres
Sebastian Baader, Jasmin Jörg
We determine the maximal number of systoles among all spheres with punctures endowed with a complete Riemannian metric of finite area.
On the crossing number of arithmetic curve systems
Sebastian Baader, Claire Burrin, Luca Studer
We show that the family of systoles of hyperbolic surfaces associated with congruence lattices in have asymptotically minimal crossing number.