The random graph embeds in the curve graph of any infinite genus surface
Geometric Topology
2016-12-20 v2
Abstract
The random graph is an infinite graph with the universal property that any embedding of extends to an embedding of , for any finite graph. In this paper we show that this graph embeds in the curve graph of a surface if and only if has infinite genus, showing that the curve system on an infinite genus surface is "as complicated as possible".
Cite
@article{arxiv.1405.6423,
title = {The random graph embeds in the curve graph of any infinite genus surface},
author = {Edgar A. Bering and Jonah Gaster},
journal= {arXiv preprint arXiv:1405.6423},
year = {2016}
}
Comments
7 pages, 4 figures. New version has a stronger result and is essentially the accepted version