Volume 17, issue 6 (2017)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Uniform fellow traveling between surgery paths in the sphere graph

Matt Clay, Yulan Qing and Kasra Rafi

Algebraic & Geometric Topology 17 (2017) 3751–3778
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
sphere graph, Guirardel core, surgery path
Mathematical Subject Classification 2010
Primary: 20E36
References
Publication
Received: 29 October 2016
Revised: 24 February 2017
Accepted: 9 April 2017
Published: 4 October 2017
Authors
Matt Clay
Department of Mathematical Sciences
University of Arkansas
Fayetteville, AR
United States
http://comp.uark.edu/~mattclay
Yulan Qing
Department of Mathematics
University of Toronto
Toronto, ON
Canada
https://sites.google.com/site/yulanqing/home
Kasra Rafi
Department of Mathematics
University of Toronto
Toronto, ON
Canada
http://www.math.toronto.edu/~rafi/