Sparse curve systems have intermediate growth type

2025/10/16 by Baader, Sebastian, Jörg, Jasmin, Kosanović, Danica
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2510.14429

Abstract

A system of simple closed curves on a surface of genus g is said to be sparse if their average pairwise intersection number does not exceed one. We show that the maximal size of a sparse curve systems grows roughly like a function of type c^√(g), with c between 2 and 81938.

Citations

• From arcs to curves: quadratic growth of 1-systems
• Crossing number inequalities for curves on surfaces
• On the crossing number of arithmetic curve systems

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