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2017 Uniform fellow traveling between surgery paths in the sphere graph
Matt Clay, Yulan Qing, Kasra Rafi
Algebr. Geom. Topol. 17(6): 3751-3778 (2017). DOI: 10.2140/agt.2017.17.3751

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.

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Matt Clay. Yulan Qing. Kasra Rafi. "Uniform fellow traveling between surgery paths in the sphere graph." Algebr. Geom. Topol. 17 (6) 3751 - 3778, 2017. https://doi.org/10.2140/agt.2017.17.3751

Information

Received: 29 October 2016; Revised: 24 February 2017; Accepted: 9 April 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06791661
MathSciNet: MR3709659
Digital Object Identifier: 10.2140/agt.2017.17.3751

Subjects:
Primary: 20E36

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 6 • 2017
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