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We consider the curve graph in the cases where it is not a Farey graph, andshow that its Gromov boundary is linearly connected. For a fixed center point cand radius r, we define the sphere of radius r to be the induced subgraph onthe set of vertices of distance r from c. We show that these spheres are alwaysconnected in high enough complexity, and prove a slightly weaker result for lowcomplexity surfaces.

Spheres in the curve complex and linear connectivity of the Gromov boundary