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Uniform fellow
traveling between surgery paths in the sphere graph
Matt Clay, Yulan Qing and Kasra Rafi |
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Algebraic & Geometric Topology 17 (2017) 3751–3778
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Abstract |
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We show that the Hausdorff distance between any forward and any backward surgery paths in the sphere graph is at most . 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 . 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
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Mathematical Subject Classification 2010
Primary: 20E36
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References |
Publication
Received: 29 October 2016
Revised: 24 February 2017
Accepted: 9 April 2017
Published: 4 October 2017
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Authors |
| Matt Clay | |
| Department of Mathematical
Sciences University of Arkansas Fayetteville, AR United States |
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| http://comp.uark.edu/~mattclay | |
| Yulan Qing | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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| https://sites.google.com/site/yulanqing/home | |
| Kasra Rafi | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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| http://www.math.toronto.edu/~rafi/ | |
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