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

2023/09/19 by Heinonen, Helena, Klein-Seetharaman, Roshan, Sun, Minghan
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2309.10690

Abstract

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.

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