Spotted disk and sphere graphs I
Geometric Topology
2021-06-11 v1
Abstract
The disk graph of a handlebody H of genus g at least 2 with m marked points on the boundary is the graph whose vertices are isotopy classes of disks disjoint from the marked points and where two vertices are connected by an edge if they can be realized disjointly. We show that for m=1 the disk graph contains quasi-isometrically embedded copies of R^2. The same holds true for the sphere graph of the double handlebody with one marked point provided that g is even.
Cite
@article{arxiv.2106.05663,
title = {Spotted disk and sphere graphs I},
author = {Ursula Hamenstädt},
journal= {arXiv preprint arXiv:2106.05663},
year = {2021}
}
Comments
19 pages, 1 figure; final version