Projections of the sphere graph to the arc graph of a surface

Brian H. Bowditch, Francesca Iezzi

Let S be a compact surface, and M be the double of a handlebody. Given a homotopy class of maps from S to M inducing an isomorphism of fundamental groups, we describe a canonical uniformly lipschitz retraction of the sphere graph of M to the arc graph of S. We also show that this retraction is a uniformly bounded distance from the nearest point projection map.

J. Topol. Anal. 10 (2018) 245-261.


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