Let S be a genus g orientable surface with c boundary components and p punctures. Then  denotes the 0-skeleton of the curve complex of S. This paper presents the following results:

(1) If   then, there exist  such that  and the number of the geodesics joining  and  is exactly 2.

(2) If   or  then, there exist   such that  and the number of the geodesics joining  and  is exactly 3.

curve complex, geodesics, subsurface projection.

Received: March 13, 2024; Accepted: April 12, 2024; Published: May 16, 2024

How to cite this article: Kanako Oie, On finiteness of the geodesics joining a pair of points in curve complex, JP Journal of Geometry and Topology 30(1) (2024), 69-82. https://doi.org/10.17654/0972415X24005

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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