Projections of the sphere graph to the arc graph of a surface
Geometric Topology
2016-07-27 v2
Abstract
Let S be a compact surface, and M be the double of a handlebody. Given a homotopy class of maps from S to M inducing an isomorphism of fundamental groups, we describe a canonical uniformly lipschitz retraction of the sphere graph of M to the arc graph of S. We also show that this retraction is a uniformly bounded distance from the nearest point projection map.
Cite
@article{arxiv.1512.04420,
title = {Projections of the sphere graph to the arc graph of a surface},
author = {Brian H. Bowditch and Francesca Iezzi},
journal= {arXiv preprint arXiv:1512.04420},
year = {2016}
}