New York Journal of Mathematics
Volume 30 (2024), 351-368


Helena Heinonen, Roshan Klein-Seetharaman, and Minghan Sun

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

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Published: March 8, 2024.
Keywords: Curve graph, connectivity, spheres.
Subject [2010]: 57M15, 57M50.

Answering a question of Wright, we show that spheres of any radius are always connected in the curve graph of surfaces Σ2,0, Σ1,3, and Σ0,6, and the union of two consecutive spheres is always connected for Σ0, 5 and Σ1,2. We also classify the connected components of spheres of radius 2 in the curve graph of Σ0,5 and Σ1,2.


All authors are funded by NSF grant DMS-2142712.

Author information

Helena Heinonen
Department of Mathematics
McGill University
805 Sherbrooke Street West Montreal
Quebec, Canada


Roshan Klein-Seetharaman
Department of Mathematics
Yale University
219 Prospect St
New Haven, CT 06511, USA


Minghan Sun
Department of Mathematics
University of Chicago
5734 S University Ave
Chicago, IL 60637, USA