Optimal connectivity results for spheres in the curve graph of low and medium complexity surfaces
Answering a question of Wright, we show that spheres of any radius are always connected in the curve graph of surfaces $Σ_{2,0}, Σ_{1,3},$ and $Σ_{0,6}$, and the union of two consecutive spheres is always connected for $Σ_{0, 5}$ and $Σ_{1,2}$. We also classify the connected components of spheres of radius 2 in the curve graph of $Σ_{0, 5}$ and $Σ_{1,2}$.
math.GT↗