Uniform fellow traveling between surgery paths in the sphere graph
Matt Clay, Yulan Qing, Kasra Rafi

TL;DR
This paper proves that the Hausdorff distance between certain surgery paths in the sphere graph is bounded, using properties of the Guirardel core and Rips moves, revealing uniform fellow traveling behavior.
Contribution
It establishes uniform bounds on the Hausdorff distance between surgery paths in the sphere graph, connecting surgeries to Rips moves on the Guirardel core.
Findings
Hausdorff distance between forward and backward surgery paths is at most 2
Hausdorff distance between any two surgery paths with same endpoints is at most 4
Surgery corresponds to Rips moves on the Guirardel core
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
