Optimal connectivity results for spheres in the curve graph of low and medium complexity surfaces

Helena Heinonen, Roshan Klein-Seetharaman, Minghan Sun

Answering a question of Wright, we show that spheres of any radius are always connected in the curve graph of surfaces ${\Sigma }_{2,0},{\Sigma }_{1,3},$ and ${\Sigma }_{0,6}$, and the union of two conse…