The random graph embeds in the curve graph of any infinite genus surface

2014/05/25 by Bering, Edgar A., Gaster, Jonah
#57M15 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1405.6423

Abstract

The random graph is an infinite graph with the universal property that any embedding of G-v extends to an embedding of G, for any finite graph. In this paper we show that this graph embeds in the curve graph of a surface Σ if and only if Σ has infinite genus, showing that the curve system on an infinite genus surface is "as complicated as possible".

Related

• The genus of curve, pants and flip graphs
• Random graphs embeddable in order-dependent surfaces
• Curve graphs on surfaces of infinite type
• The expected genus of a random chord diagram
• On the Genus of a Random Riemann Surface