Geodesic
Uniform fellow traveling between surgery paths in the sphere graph
Clay, Matt1 ; Qing, Yulan2 ; Rafi, Kasra2
1 Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, United States
2 Department of Mathematics, University of Toronto, Toronto, ON, Canada
Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3751-3778

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2017.17.3751
Classification : 20E36
Keywords: sphere graph, Guirardel core, surgery path

Clay, Matt 1 ; Qing, Yulan 2 ; Rafi, Kasra 2

1 Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, United States
2 Department of Mathematics, University of Toronto, Toronto, ON, Canada 
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Clay, Matt; Qing, Yulan; Rafi, Kasra. Uniform fellow traveling between surgery paths in the sphere graph. Algebraic and Geometric Topology, Tome 17 (2017) no. 6, pp. 3751-3778. doi: 10.2140/agt.2017.17.3751

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