Uniform fellow traveling between surgery paths in the sphere graph
Group Theory
2018-03-16 v3 Geometric Topology
Abstract
We show that the Hausdorff distance between any forward and any backward surgery paths in the sphere graph is at most 2. From this it follows that the Hausdorff distance between any two surgery paths with the same initial sphere system and same target sphere system is at most 4. Our proof relies on understanding how surgeries affect the Guirardel core associated to sphere systems. We show that applying a surgery is equivalent to performing a Rips move on the Guirardel core.
Keywords
Cite
@article{arxiv.1610.05832,
title = {Uniform fellow traveling between surgery paths in the sphere graph},
author = {Matt Clay and Yulan Qing and Kasra Rafi},
journal= {arXiv preprint arXiv:1610.05832},
year = {2018}
}
Comments
20 pages, 7 figures; v2: rewrote introduction and updated references; v3: minor edits