 

Helena Heinonen,
Roshan KleinSeetharaman, 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. 


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}.


Acknowledgements
All authors are funded by NSF grant DMS2142712.


Author information
Helena Heinonen
Department of Mathematics
McGill University
805 Sherbrooke Street West Montreal
Quebec, Canada
helenasheinonen@gmail.com
Roshan KleinSeetharaman
Department of Mathematics
Yale University
219 Prospect St
New Haven, CT 06511, USA
roshan.kleinseetharaman@gmail.com
Minghan Sun
Department of Mathematics
University of Chicago
5734 S University Ave
Chicago, IL 60637, USA
minghansun250@gmail.com

